RS Aggarwal Solutions: Exercise 7D - Factorisation | Mathematics (Maths) Class 8 PDF Download

 Page 1


    
 
    
                         
      
Q u e s t i o n : 7 6
Factorise:
x
2
 + 5x + 6
S o l u t i o n :
The given expression is x
2
+ 5x + 6. Find two numbers that follow the conditions given below: Sum = 5 Product = 6Clearly, the numbers are 3 and 2. x
2
+ 5x + 6 =  x
2
+ 3x + 2x + 6      
Q u e s t i o n : 7 7
Factorise:
y
2
 + 10y + 24
S o l u t i o n :
The given expression is y
2
+ 10y + 24. Find two numbers that follow the conditions given below: Sum = 10 Product = 24Clearly, the numbers are 6 and 4. y
2
+ 10y + 24 =  y
2
+ 6y + 4y
Q u e s t i o n : 7 8
Factorise:
z
2
 + 12z + 27
S o l u t i o n :
The given expression is z
2
+ 12z + 27. Find two numbers that follow the conditions given below: Sum = 12 Product = 27Clearly, the numbers are 9 and 3. z
2
+ 12z + 27 = z
2
+ 9z + 3z 
Q u e s t i o n : 7 9
Factorise:
p
2
 + 6p + 8
S o l u t i o n :
The given expression is p
2
+ 6p + 8. Find two numbers that follow the conditions given below: Sum = 6 Product = 8Clearly, the numbers are 4 and 2. p
2
+ 6p + 8 =  p
2
+ 4p + 2p +8     
Q u e s t i o n : 8 0
Factorise:
x
2
 + 15x + 56
S o l u t i o n :
The given expression is x
2
+ 15x + 56. Find two numbers that follow the conditions given below: Sum = 15 Product = 56Clearly, the numbers are 8 and 7. x
2
+ 15x + 56 = x
2
+ 8x + 7x 
Q u e s t i o n : 8 1
Factorise:
y
2
 + 19y + 60
S o l u t i o n :
The given expression is y
2
+ 19y + 60. Find two numbers that follow the conditions given below: Sum = 19 Product = 60Clearly, the numbers are 15 and 4. y
2
+ 19y + 60 = y
2
+ 15y + 4
Q u e s t i o n : 8 2
Factorise:
x
2
 + 13x + 40
S o l u t i o n :
The given expression is x
2
+ 13x + 40. Find two numbers that follow the conditions given below: Sum = 13 Product = 40Clearly, the numbers are 8 and 5. x
2
+ 13x + 40 = x
2
+ 8x + 5x 
Q u e s t i o n : 8 3
Factorise:
q
2
 - 10q + 21
S o l u t i o n :
The given expression is q
2
-10q + 21. Find two numbers that follow the conditions given below: Sum = -10 Product = 21Clearly, the numbers are -7 and -3. q
2
-10q + 21 = q
2
-7q -3q + 
Q u e s t i o n : 8 4
Factorise:
p
2
 + 6p - 16
S o l u t i o n :
The given expression is p
2
+ 6p -16. Find two numbers that follow the conditions given below: Sum = 6 Product = -16Clearly, the numbers are 8 and -2. p
2
+ 6p -16 =  p
2
+8p -2p -16   
Q u e s t i o n : 8 5
Factorise:
x
2
 - 10x + 24
S o l u t i o n :
The given expression is x
2
-10x +24. Find two numbers that follow the conditions given below: Sum = -10 Product = 24Clearly, the numbers are -6 and -4. x
2
-10x +24 =  x
2
-6x -4x +24
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Q u e s t i o n : 7 6
Factorise:
x
2
 + 5x + 6
S o l u t i o n :
The given expression is x
2
+ 5x + 6. Find two numbers that follow the conditions given below: Sum = 5 Product = 6Clearly, the numbers are 3 and 2. x
2
+ 5x + 6 =  x
2
+ 3x + 2x + 6      
Q u e s t i o n : 7 7
Factorise:
y
2
 + 10y + 24
S o l u t i o n :
The given expression is y
2
+ 10y + 24. Find two numbers that follow the conditions given below: Sum = 10 Product = 24Clearly, the numbers are 6 and 4. y
2
+ 10y + 24 =  y
2
+ 6y + 4y
Q u e s t i o n : 7 8
Factorise:
z
2
 + 12z + 27
S o l u t i o n :
The given expression is z
2
+ 12z + 27. Find two numbers that follow the conditions given below: Sum = 12 Product = 27Clearly, the numbers are 9 and 3. z
2
+ 12z + 27 = z
2
+ 9z + 3z 
Q u e s t i o n : 7 9
Factorise:
p
2
 + 6p + 8
S o l u t i o n :
The given expression is p
2
+ 6p + 8. Find two numbers that follow the conditions given below: Sum = 6 Product = 8Clearly, the numbers are 4 and 2. p
2
+ 6p + 8 =  p
2
+ 4p + 2p +8     
Q u e s t i o n : 8 0
Factorise:
x
2
 + 15x + 56
S o l u t i o n :
The given expression is x
2
+ 15x + 56. Find two numbers that follow the conditions given below: Sum = 15 Product = 56Clearly, the numbers are 8 and 7. x
2
+ 15x + 56 = x
2
+ 8x + 7x 
Q u e s t i o n : 8 1
Factorise:
y
2
 + 19y + 60
S o l u t i o n :
The given expression is y
2
+ 19y + 60. Find two numbers that follow the conditions given below: Sum = 19 Product = 60Clearly, the numbers are 15 and 4. y
2
+ 19y + 60 = y
2
+ 15y + 4
Q u e s t i o n : 8 2
Factorise:
x
2
 + 13x + 40
S o l u t i o n :
The given expression is x
2
+ 13x + 40. Find two numbers that follow the conditions given below: Sum = 13 Product = 40Clearly, the numbers are 8 and 5. x
2
+ 13x + 40 = x
2
+ 8x + 5x 
Q u e s t i o n : 8 3
Factorise:
q
2
 - 10q + 21
S o l u t i o n :
The given expression is q
2
-10q + 21. Find two numbers that follow the conditions given below: Sum = -10 Product = 21Clearly, the numbers are -7 and -3. q
2
-10q + 21 = q
2
-7q -3q + 
Q u e s t i o n : 8 4
Factorise:
p
2
 + 6p - 16
S o l u t i o n :
The given expression is p
2
+ 6p -16. Find two numbers that follow the conditions given below: Sum = 6 Product = -16Clearly, the numbers are 8 and -2. p
2
+ 6p -16 =  p
2
+8p -2p -16   
Q u e s t i o n : 8 5
Factorise:
x
2
 - 10x + 24
S o l u t i o n :
The given expression is x
2
-10x +24. Find two numbers that follow the conditions given below: Sum = -10 Product = 24Clearly, the numbers are -6 and -4. x
2
-10x +24 =  x
2
-6x -4x +24
Q u e s t i o n : 8 6
Factorise:
x
2
 - 23x + 42
S o l u t i o n :
The given expression is x
2
-23x + 42. Find two numbers that follow the conditions given below: Sum = -23 Product = 42Clearly, the numbers are -21 and -2. x
2
-23x + 42 =  x
2
-21x -2x
Q u e s t i o n : 8 7
Factorise:
x
2
 - 17x + 16
S o l u t i o n :
The given expression is x
2
-17x + 16. Find two numbers that follow the conditions given below: Sum = -17 Product = 16Clearly, the numbers are -16 and -1. x
2
-17x + 16 =  x
2
-16x -x 
Q u e s t i o n : 8 8
Factorise:
y
2
 - 21y + 90
S o l u t i o n :
The given expression is y
2
-21y + 90. Find two numbers that follow the conditions given below: Sum = -21 Product = 90Clearly, the numbers are -15 and -6. y
2
-21y + 90 = y
2
-15y -6y 
Q u e s t i o n : 8 9
Factorise:
x
2
 - 22x + 117
S o l u t i o n :
The given expression is x
2
-22x + 117. Find two numbers that follow the conditions given below: Sum = -22 Product = 117Clearly, the numbers are -13 and -9. x
2
-22x + 117 =  x
2
-13x
Q u e s t i o n : 9 0
Factorise:
x
2
 - 9x + 20
S o l u t i o n :
The given expression is x
2
-9x + 20. Find two numbers that follow the conditions given below: Sum = -9 Product = 20Clearly, the numbers are -5 and -4. x
2
-9x + 20 =   x
2
-5x -4x + 20
Q u e s t i o n : 9 1
Factorise:
x
2
 + x - 132
S o l u t i o n :
The given expression is x
2
+x -132. Find two numbers that follow the conditions given below: Sum = 1 and pProduct = -132Clearly, the numbers are 12 and -11. x
2
+ x -132 =  x
2
+12x
Q u e s t i o n : 9 2
Factorise:
x
2
 + 5x - 104
S o l u t i o n :
The given expression is x
2
+5x -104. Find two numbers that follow the conditions given below: Sum = 5 Product = -104Clearly, the numbers are 13 and -8. x
2
+5x -104 =  x
2
+13x -8x -
Q u e s t i o n : 9 3
Factorise:
y
2
 + 7y - 144
S o l u t i o n :
The given expression is y
2
+7y -144. Find two numbers that follow the conditions given below: Sum = 7 Product = -144Clearly, the numbers are 16 and -9. y
2
+7y -144 = y
2
+16y -9y -144
Q u e s t i o n : 9 4
Factorise:
z
2
 + 19z - 150
S o l u t i o n :
The given expression is z
2
+19z -150. Find two numbers that follow the conditions given below: Sum = 19 Product = -150Clearly, the numbers are 25 and -6. z
2
+19z -150 = z
2
+25z -6
Q u e s t i o n : 9 5
Factorise:
y
2
 + y - 72
S o l u t i o n :
The given expression is y
2
+y -72. Find two numbers that follow the conditions given below: Sum = 1 Product = -72Clearly, the numbers are 9 and -8. y
2
+y -72 =  y
2
+9y -8y -72         
Q u e s t i o n : 9 6
Factorise:
a
2
 + 6a - 91
S o l u t i o n :
The given expression is a
2
+6a -91. Find two numbers that follow the conditions given below: Sum = 6 Product = -91Clearly, the numbers are 13 and -7. a
2
+6a -91 =  a
2
+13a -7a -91  
Q u e s t i o n : 9 7
Factorise:
p
2
 - 4p - 77
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Q u e s t i o n : 7 6
Factorise:
x
2
 + 5x + 6
S o l u t i o n :
The given expression is x
2
+ 5x + 6. Find two numbers that follow the conditions given below: Sum = 5 Product = 6Clearly, the numbers are 3 and 2. x
2
+ 5x + 6 =  x
2
+ 3x + 2x + 6      
Q u e s t i o n : 7 7
Factorise:
y
2
 + 10y + 24
S o l u t i o n :
The given expression is y
2
+ 10y + 24. Find two numbers that follow the conditions given below: Sum = 10 Product = 24Clearly, the numbers are 6 and 4. y
2
+ 10y + 24 =  y
2
+ 6y + 4y
Q u e s t i o n : 7 8
Factorise:
z
2
 + 12z + 27
S o l u t i o n :
The given expression is z
2
+ 12z + 27. Find two numbers that follow the conditions given below: Sum = 12 Product = 27Clearly, the numbers are 9 and 3. z
2
+ 12z + 27 = z
2
+ 9z + 3z 
Q u e s t i o n : 7 9
Factorise:
p
2
 + 6p + 8
S o l u t i o n :
The given expression is p
2
+ 6p + 8. Find two numbers that follow the conditions given below: Sum = 6 Product = 8Clearly, the numbers are 4 and 2. p
2
+ 6p + 8 =  p
2
+ 4p + 2p +8     
Q u e s t i o n : 8 0
Factorise:
x
2
 + 15x + 56
S o l u t i o n :
The given expression is x
2
+ 15x + 56. Find two numbers that follow the conditions given below: Sum = 15 Product = 56Clearly, the numbers are 8 and 7. x
2
+ 15x + 56 = x
2
+ 8x + 7x 
Q u e s t i o n : 8 1
Factorise:
y
2
 + 19y + 60
S o l u t i o n :
The given expression is y
2
+ 19y + 60. Find two numbers that follow the conditions given below: Sum = 19 Product = 60Clearly, the numbers are 15 and 4. y
2
+ 19y + 60 = y
2
+ 15y + 4
Q u e s t i o n : 8 2
Factorise:
x
2
 + 13x + 40
S o l u t i o n :
The given expression is x
2
+ 13x + 40. Find two numbers that follow the conditions given below: Sum = 13 Product = 40Clearly, the numbers are 8 and 5. x
2
+ 13x + 40 = x
2
+ 8x + 5x 
Q u e s t i o n : 8 3
Factorise:
q
2
 - 10q + 21
S o l u t i o n :
The given expression is q
2
-10q + 21. Find two numbers that follow the conditions given below: Sum = -10 Product = 21Clearly, the numbers are -7 and -3. q
2
-10q + 21 = q
2
-7q -3q + 
Q u e s t i o n : 8 4
Factorise:
p
2
 + 6p - 16
S o l u t i o n :
The given expression is p
2
+ 6p -16. Find two numbers that follow the conditions given below: Sum = 6 Product = -16Clearly, the numbers are 8 and -2. p
2
+ 6p -16 =  p
2
+8p -2p -16   
Q u e s t i o n : 8 5
Factorise:
x
2
 - 10x + 24
S o l u t i o n :
The given expression is x
2
-10x +24. Find two numbers that follow the conditions given below: Sum = -10 Product = 24Clearly, the numbers are -6 and -4. x
2
-10x +24 =  x
2
-6x -4x +24
Q u e s t i o n : 8 6
Factorise:
x
2
 - 23x + 42
S o l u t i o n :
The given expression is x
2
-23x + 42. Find two numbers that follow the conditions given below: Sum = -23 Product = 42Clearly, the numbers are -21 and -2. x
2
-23x + 42 =  x
2
-21x -2x
Q u e s t i o n : 8 7
Factorise:
x
2
 - 17x + 16
S o l u t i o n :
The given expression is x
2
-17x + 16. Find two numbers that follow the conditions given below: Sum = -17 Product = 16Clearly, the numbers are -16 and -1. x
2
-17x + 16 =  x
2
-16x -x 
Q u e s t i o n : 8 8
Factorise:
y
2
 - 21y + 90
S o l u t i o n :
The given expression is y
2
-21y + 90. Find two numbers that follow the conditions given below: Sum = -21 Product = 90Clearly, the numbers are -15 and -6. y
2
-21y + 90 = y
2
-15y -6y 
Q u e s t i o n : 8 9
Factorise:
x
2
 - 22x + 117
S o l u t i o n :
The given expression is x
2
-22x + 117. Find two numbers that follow the conditions given below: Sum = -22 Product = 117Clearly, the numbers are -13 and -9. x
2
-22x + 117 =  x
2
-13x
Q u e s t i o n : 9 0
Factorise:
x
2
 - 9x + 20
S o l u t i o n :
The given expression is x
2
-9x + 20. Find two numbers that follow the conditions given below: Sum = -9 Product = 20Clearly, the numbers are -5 and -4. x
2
-9x + 20 =   x
2
-5x -4x + 20
Q u e s t i o n : 9 1
Factorise:
x
2
 + x - 132
S o l u t i o n :
The given expression is x
2
+x -132. Find two numbers that follow the conditions given below: Sum = 1 and pProduct = -132Clearly, the numbers are 12 and -11. x
2
+ x -132 =  x
2
+12x
Q u e s t i o n : 9 2
Factorise:
x
2
 + 5x - 104
S o l u t i o n :
The given expression is x
2
+5x -104. Find two numbers that follow the conditions given below: Sum = 5 Product = -104Clearly, the numbers are 13 and -8. x
2
+5x -104 =  x
2
+13x -8x -
Q u e s t i o n : 9 3
Factorise:
y
2
 + 7y - 144
S o l u t i o n :
The given expression is y
2
+7y -144. Find two numbers that follow the conditions given below: Sum = 7 Product = -144Clearly, the numbers are 16 and -9. y
2
+7y -144 = y
2
+16y -9y -144
Q u e s t i o n : 9 4
Factorise:
z
2
 + 19z - 150
S o l u t i o n :
The given expression is z
2
+19z -150. Find two numbers that follow the conditions given below: Sum = 19 Product = -150Clearly, the numbers are 25 and -6. z
2
+19z -150 = z
2
+25z -6
Q u e s t i o n : 9 5
Factorise:
y
2
 + y - 72
S o l u t i o n :
The given expression is y
2
+y -72. Find two numbers that follow the conditions given below: Sum = 1 Product = -72Clearly, the numbers are 9 and -8. y
2
+y -72 =  y
2
+9y -8y -72         
Q u e s t i o n : 9 6
Factorise:
a
2
 + 6a - 91
S o l u t i o n :
The given expression is a
2
+6a -91. Find two numbers that follow the conditions given below: Sum = 6 Product = -91Clearly, the numbers are 13 and -7. a
2
+6a -91 =  a
2
+13a -7a -91  
Q u e s t i o n : 9 7
Factorise:
p
2
 - 4p - 77
S o l u t i o n :
The given expression is p
2
-4p -77. Find two numbers that follow the conditions given below: Sum = -4 Product = -77Clearly, the numbers are -11 and 7. p
2
-4p -77 =  p
2
-11p +7p -77  
Q u e s t i o n : 9 8
Factorise:
x
2
 - 7x - 30
S o l u t i o n :
The given expression is x
2
-7x -30. Find two numbers that follow the conditions given below: Sum = -7 Product = -30Clearly, the numbers are -10 and 3. x
2
-7x -30 =   x
2
-10x +3x -30
Q u e s t i o n : 9 9
Factorise:
x
2
 - 11x - 42
S o l u t i o n :
The given expression is x
2
-11x -42. Find two numbers that follow the conditions given below: Sum = -11 Product = -42Clearly, the numbers are -14 and 3. x
2
-11x -42 =   x
2
-14x +3x 
Q u e s t i o n : 1 0 0
Factorise:
x
2
 - 5x - 24
S o l u t i o n :
The given expression is x
2
-5x -24. Find two numbers that follow the conditions given below: Sum = -5 Product = -24Clearly, the numbers are -8 and 3. x
2
-5x -24 =   x
2
-8x +3x -24     
Q u e s t i o n : 1 0 1
Factorise:
y
2
 - 6y - 135
S o l u t i o n :
The given expression is y
2
-6y -135. Find two numbers that follow the conditions given below: Sum = -6 Product = -135Clearly, the numbers are -15 and 9. y
2
-6y -135 =   y
2
-15y +9y 
Q u e s t i o n : 1 0 2
Factorise:
z
2
 - 12z - 45
S o l u t i o n :
The given expression is z
2
-12z -45. Find two numbers that follow the conditions given below: Sum = -12 Product = -45Clearly, the numbers are -15 and 3. z
2
-12z -45 =    z
2
-15z +3z
Q u e s t i o n : 1 0 3
Factorise:
x
2
 - 4x - 12
S o l u t i o n :
The given expression is x
2
-4x -12. Find two numbers that follow the conditions given below: Sum = -4 Product = -12Clearly, the numbers are -6 and 2. x
2
-4x -12 =   x
2
-6x +2x -12    
Q u e s t i o n : 1 0 4
Factorise:
3x
2
 + 10x + 8
S o l u t i o n :
The given expression is 3x
2
+10x +8. Find two numbers that follow the conditions given below: Sum = 10Product = 3 ×8 = 24Clearly, the numbers are 6 and 4. 3x
2
+10x +8 =  3x
2
+10x 
Q u e s t i o n : 1 0 5
Factorise:
3y
2
 + 14y + 8
S o l u t i o n :
The given expression is 3y
2
+14y +8Find two numbers that follow the conditions given below: Sum = 14 Product = 24Clearly, the numbers are 12 and 2. 3y
2
+14y +8 = 3y
2
+12y +2y +8
Q u e s t i o n : 1 0 6
Factorise:
3z
2
 - 10z + 8
S o l u t i o n :
The given expression is 3z
2
-10z +8. Find two numbers that follow the conditions given below: Sum = -10 Product = 3 ×8 = 24Clearly, the numbers are -6 and -4. 3z
2
-10z +8 =  3z
2
-6z
Q u e s t i o n : 1 0 7
Factorise:
2x
2
 + x - 45
S o l u t i o n :
The given expression is 2x
2
+x -45. Find two numbers that follow the conditions given below: Sum = 1 Product = -45 ×2 = -90Clearly, the numbers are 10 and -9. 2x
2
+x -45 =  2x
2
+10
Q u e s t i o n : 1 0 8
Factorise:
6p
2
 + 11p - 10
S o l u t i o n :
The given expression is 6p
2
+11p -10. Find two numbers that follow the conditions given below: Sum = 11 Product = 6 × -10 = -60Clearly, the numbers are 15 and -4. 6p
2
+11p -10 =  6
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Q u e s t i o n : 7 6
Factorise:
x
2
 + 5x + 6
S o l u t i o n :
The given expression is x
2
+ 5x + 6. Find two numbers that follow the conditions given below: Sum = 5 Product = 6Clearly, the numbers are 3 and 2. x
2
+ 5x + 6 =  x
2
+ 3x + 2x + 6      
Q u e s t i o n : 7 7
Factorise:
y
2
 + 10y + 24
S o l u t i o n :
The given expression is y
2
+ 10y + 24. Find two numbers that follow the conditions given below: Sum = 10 Product = 24Clearly, the numbers are 6 and 4. y
2
+ 10y + 24 =  y
2
+ 6y + 4y
Q u e s t i o n : 7 8
Factorise:
z
2
 + 12z + 27
S o l u t i o n :
The given expression is z
2
+ 12z + 27. Find two numbers that follow the conditions given below: Sum = 12 Product = 27Clearly, the numbers are 9 and 3. z
2
+ 12z + 27 = z
2
+ 9z + 3z 
Q u e s t i o n : 7 9
Factorise:
p
2
 + 6p + 8
S o l u t i o n :
The given expression is p
2
+ 6p + 8. Find two numbers that follow the conditions given below: Sum = 6 Product = 8Clearly, the numbers are 4 and 2. p
2
+ 6p + 8 =  p
2
+ 4p + 2p +8     
Q u e s t i o n : 8 0
Factorise:
x
2
 + 15x + 56
S o l u t i o n :
The given expression is x
2
+ 15x + 56. Find two numbers that follow the conditions given below: Sum = 15 Product = 56Clearly, the numbers are 8 and 7. x
2
+ 15x + 56 = x
2
+ 8x + 7x 
Q u e s t i o n : 8 1
Factorise:
y
2
 + 19y + 60
S o l u t i o n :
The given expression is y
2
+ 19y + 60. Find two numbers that follow the conditions given below: Sum = 19 Product = 60Clearly, the numbers are 15 and 4. y
2
+ 19y + 60 = y
2
+ 15y + 4
Q u e s t i o n : 8 2
Factorise:
x
2
 + 13x + 40
S o l u t i o n :
The given expression is x
2
+ 13x + 40. Find two numbers that follow the conditions given below: Sum = 13 Product = 40Clearly, the numbers are 8 and 5. x
2
+ 13x + 40 = x
2
+ 8x + 5x 
Q u e s t i o n : 8 3
Factorise:
q
2
 - 10q + 21
S o l u t i o n :
The given expression is q
2
-10q + 21. Find two numbers that follow the conditions given below: Sum = -10 Product = 21Clearly, the numbers are -7 and -3. q
2
-10q + 21 = q
2
-7q -3q + 
Q u e s t i o n : 8 4
Factorise:
p
2
 + 6p - 16
S o l u t i o n :
The given expression is p
2
+ 6p -16. Find two numbers that follow the conditions given below: Sum = 6 Product = -16Clearly, the numbers are 8 and -2. p
2
+ 6p -16 =  p
2
+8p -2p -16   
Q u e s t i o n : 8 5
Factorise:
x
2
 - 10x + 24
S o l u t i o n :
The given expression is x
2
-10x +24. Find two numbers that follow the conditions given below: Sum = -10 Product = 24Clearly, the numbers are -6 and -4. x
2
-10x +24 =  x
2
-6x -4x +24
Q u e s t i o n : 8 6
Factorise:
x
2
 - 23x + 42
S o l u t i o n :
The given expression is x
2
-23x + 42. Find two numbers that follow the conditions given below: Sum = -23 Product = 42Clearly, the numbers are -21 and -2. x
2
-23x + 42 =  x
2
-21x -2x
Q u e s t i o n : 8 7
Factorise:
x
2
 - 17x + 16
S o l u t i o n :
The given expression is x
2
-17x + 16. Find two numbers that follow the conditions given below: Sum = -17 Product = 16Clearly, the numbers are -16 and -1. x
2
-17x + 16 =  x
2
-16x -x 
Q u e s t i o n : 8 8
Factorise:
y
2
 - 21y + 90
S o l u t i o n :
The given expression is y
2
-21y + 90. Find two numbers that follow the conditions given below: Sum = -21 Product = 90Clearly, the numbers are -15 and -6. y
2
-21y + 90 = y
2
-15y -6y 
Q u e s t i o n : 8 9
Factorise:
x
2
 - 22x + 117
S o l u t i o n :
The given expression is x
2
-22x + 117. Find two numbers that follow the conditions given below: Sum = -22 Product = 117Clearly, the numbers are -13 and -9. x
2
-22x + 117 =  x
2
-13x
Q u e s t i o n : 9 0
Factorise:
x
2
 - 9x + 20
S o l u t i o n :
The given expression is x
2
-9x + 20. Find two numbers that follow the conditions given below: Sum = -9 Product = 20Clearly, the numbers are -5 and -4. x
2
-9x + 20 =   x
2
-5x -4x + 20
Q u e s t i o n : 9 1
Factorise:
x
2
 + x - 132
S o l u t i o n :
The given expression is x
2
+x -132. Find two numbers that follow the conditions given below: Sum = 1 and pProduct = -132Clearly, the numbers are 12 and -11. x
2
+ x -132 =  x
2
+12x
Q u e s t i o n : 9 2
Factorise:
x
2
 + 5x - 104
S o l u t i o n :
The given expression is x
2
+5x -104. Find two numbers that follow the conditions given below: Sum = 5 Product = -104Clearly, the numbers are 13 and -8. x
2
+5x -104 =  x
2
+13x -8x -
Q u e s t i o n : 9 3
Factorise:
y
2
 + 7y - 144
S o l u t i o n :
The given expression is y
2
+7y -144. Find two numbers that follow the conditions given below: Sum = 7 Product = -144Clearly, the numbers are 16 and -9. y
2
+7y -144 = y
2
+16y -9y -144
Q u e s t i o n : 9 4
Factorise:
z
2
 + 19z - 150
S o l u t i o n :
The given expression is z
2
+19z -150. Find two numbers that follow the conditions given below: Sum = 19 Product = -150Clearly, the numbers are 25 and -6. z
2
+19z -150 = z
2
+25z -6
Q u e s t i o n : 9 5
Factorise:
y
2
 + y - 72
S o l u t i o n :
The given expression is y
2
+y -72. Find two numbers that follow the conditions given below: Sum = 1 Product = -72Clearly, the numbers are 9 and -8. y
2
+y -72 =  y
2
+9y -8y -72         
Q u e s t i o n : 9 6
Factorise:
a
2
 + 6a - 91
S o l u t i o n :
The given expression is a
2
+6a -91. Find two numbers that follow the conditions given below: Sum = 6 Product = -91Clearly, the numbers are 13 and -7. a
2
+6a -91 =  a
2
+13a -7a -91  
Q u e s t i o n : 9 7
Factorise:
p
2
 - 4p - 77
S o l u t i o n :
The given expression is p
2
-4p -77. Find two numbers that follow the conditions given below: Sum = -4 Product = -77Clearly, the numbers are -11 and 7. p
2
-4p -77 =  p
2
-11p +7p -77  
Q u e s t i o n : 9 8
Factorise:
x
2
 - 7x - 30
S o l u t i o n :
The given expression is x
2
-7x -30. Find two numbers that follow the conditions given below: Sum = -7 Product = -30Clearly, the numbers are -10 and 3. x
2
-7x -30 =   x
2
-10x +3x -30
Q u e s t i o n : 9 9
Factorise:
x
2
 - 11x - 42
S o l u t i o n :
The given expression is x
2
-11x -42. Find two numbers that follow the conditions given below: Sum = -11 Product = -42Clearly, the numbers are -14 and 3. x
2
-11x -42 =   x
2
-14x +3x 
Q u e s t i o n : 1 0 0
Factorise:
x
2
 - 5x - 24
S o l u t i o n :
The given expression is x
2
-5x -24. Find two numbers that follow the conditions given below: Sum = -5 Product = -24Clearly, the numbers are -8 and 3. x
2
-5x -24 =   x
2
-8x +3x -24     
Q u e s t i o n : 1 0 1
Factorise:
y
2
 - 6y - 135
S o l u t i o n :
The given expression is y
2
-6y -135. Find two numbers that follow the conditions given below: Sum = -6 Product = -135Clearly, the numbers are -15 and 9. y
2
-6y -135 =   y
2
-15y +9y 
Q u e s t i o n : 1 0 2
Factorise:
z
2
 - 12z - 45
S o l u t i o n :
The given expression is z
2
-12z -45. Find two numbers that follow the conditions given below: Sum = -12 Product = -45Clearly, the numbers are -15 and 3. z
2
-12z -45 =    z
2
-15z +3z
Q u e s t i o n : 1 0 3
Factorise:
x
2
 - 4x - 12
S o l u t i o n :
The given expression is x
2
-4x -12. Find two numbers that follow the conditions given below: Sum = -4 Product = -12Clearly, the numbers are -6 and 2. x
2
-4x -12 =   x
2
-6x +2x -12    
Q u e s t i o n : 1 0 4
Factorise:
3x
2
 + 10x + 8
S o l u t i o n :
The given expression is 3x
2
+10x +8. Find two numbers that follow the conditions given below: Sum = 10Product = 3 ×8 = 24Clearly, the numbers are 6 and 4. 3x
2
+10x +8 =  3x
2
+10x 
Q u e s t i o n : 1 0 5
Factorise:
3y
2
 + 14y + 8
S o l u t i o n :
The given expression is 3y
2
+14y +8Find two numbers that follow the conditions given below: Sum = 14 Product = 24Clearly, the numbers are 12 and 2. 3y
2
+14y +8 = 3y
2
+12y +2y +8
Q u e s t i o n : 1 0 6
Factorise:
3z
2
 - 10z + 8
S o l u t i o n :
The given expression is 3z
2
-10z +8. Find two numbers that follow the conditions given below: Sum = -10 Product = 3 ×8 = 24Clearly, the numbers are -6 and -4. 3z
2
-10z +8 =  3z
2
-6z
Q u e s t i o n : 1 0 7
Factorise:
2x
2
 + x - 45
S o l u t i o n :
The given expression is 2x
2
+x -45. Find two numbers that follow the conditions given below: Sum = 1 Product = -45 ×2 = -90Clearly, the numbers are 10 and -9. 2x
2
+x -45 =  2x
2
+10
Q u e s t i o n : 1 0 8
Factorise:
6p
2
 + 11p - 10
S o l u t i o n :
The given expression is 6p
2
+11p -10. Find two numbers that follow the conditions given below: Sum = 11 Product = 6 × -10 = -60Clearly, the numbers are 15 and -4. 6p
2
+11p -10 =  6
Q u e s t i o n : 1 0 9
Factorise:
2x
2
 - 17x - 30
S o l u t i o n :
The given expression is 2x
2
-17x -30. Find two numbers that follow the conditions given below: Sum = -17 Product = -30 ×2 = -60Clearly, the numbers are -20 and 3. 2x
2
-17x -30 =  2
Q u e s t i o n : 1 1 0
Factorise:
7y
2
 - 19y - 6
S o l u t i o n :
The given expression is 7y
2
-19y -6. Find two numbers that follow the conditions given below: Sum = -19 Product = 7 × -6 = -42Clearly, the numbers are -21 and 2. 7y
2
-19y -6 = 7y
2
-21
Q u e s t i o n : 1 1 1
Factorise:
28 - 31x - 5x
2
S o l u t i o n :
The given expression is 28 -31x -5x
2
. Find two numbers that follow the conditions given below: Sum = -31Product = 28 × -5 = -140Clearly, the numbers are -35 and 4. 28 -31x -5x
2
= 28
Q u e s t i o n : 1 1 2
Factorise:
3 + 23z - 8z
2
S o l u t i o n :
The given expression is 3 +23z -8z
2
. Find two numbers that follow the conditions given below: Sum = 23  Product = 3 × -8 = -24Clearly, the numbers are 24 and -1. 3 +23z -8z
2
= 3 +24
Q u e s t i o n : 1 1 3
Factorise:
6x
2
 - 5x - 6
S o l u t i o n :
The given expression is 6x
2
-5x -6. Find two numbers that follow the conditions given below: Sum = -5 Product = -6 ×6 = -36Clearly, the numbers are -9 and 4. 6x
2
-5x -6 = 6x
2
-9x +4x
Q u e s t i o n : 1 1 4
Factorise:
3m
2
 + 24m + 36
S o l u t i o n :
The given expression is 3m2+24m +36.Find two numbers that follow the conditions given below:Sum =24 Product =36×3=108Clearly, the numbers are 18 and 6.3m2+24m +36= 3m2+18m
                             = 3m(m+6)+6(m+6)                              =(3m+6) (m+6)=3m+2m+6                              
Q u e s t i o n : 1 1 5
Factorise:
4n
2
 - 8n + 3
S o l u t i o n :
The given expression is 4n2-8n +3.Find two numbers that follow the conditions given below:Sum =-8 Product =4×3=12Clearly, the numbers are -6 and -2.4n2-8n +3=4n2-2n -6n+3              
                      =(2n-1) (2n-3)                              
Q u e s t i o n : 1 1 6
Factorise:
6x
2
 - 17x - 3
S o l u t i o n :
The given expression is 6x2-17x-3.Find two numbers that follow the conditions given below:Sum =-17 Product = 6×-3=-18Clearly, the numbers are -18 and 1.6x2-17x-3=6x2-18x+x-3         
                      =(6x+1) (x-3)                              
Q u e s t i o n : 1 1 7
Factorise:
7x
2
 - 19x - 6
S o l u t i o n :
The given expression is 7x2-19x-6.Find two numbers that follow the conditions given below: Sum =-19 Product =7×-6=-42Clearly, the numbers are -21 and 2.7x2-19x-6=7x2-21x+2x-6       
                      =(7x+2) (x-3)