Factorization - Exercise 7.7 | Mathematics (Maths) Class 8 PDF Download

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Q u e s t i o n : 1 4 7
Factorize each of the following algebraic expression:
x
2
 + 12x - 45
S o l u t i o n :
To factorise x2+12x-45, we will find two numbers p and q such that p+q=12 and pq=-45.Now, 15+(-3)=12 and 15×(-3)=-45Splitting the middle term 12x in the given quadratic as -3x+15x, we
 x2+12x-45=x2-3x+15x-45                       =(x2-3x)+(15x-45)                       =x(x-3)+15(x-3)                       =(x+15)(x-3)
Q u e s t i o n : 1 4 8
Factorize each of the following algebraic expression:
40 + 3x - x
2
S o l u t i o n :
We have:40+3x-x2 ?-(x2-3x-40) To factorise (x2-3x-40), we will find two numbers p and q such that p+q=-3 and pq=-40.Now,  5+(-8)=-3 and 5×(-8)=-40Splitting the middle term -3x in the given
40+3x-x2=-(x2-3x-40)                    =-(x2+5x-8x-40)                    =-[(x2+5x)-(8x+40)]                    =-[x(x+5)-8(x+5)]                    =-(x-8)(x+5)                    =(x+5)(-x+8)
Q u e s t i o n : 1 4 9
Factorize each of the following algebraic expression:
a
2
 + 3a - 88
S o l u t i o n :
To factorise a2+3a-88, we will find two numbers p and q such that p+q=3 and pq=-88.Now,  11+(-8)=3 and 11×(-8)=-88Splitting the middle term 3a in the given quadratic as 11a-8a, we get:a
                    =(a2+11a)-(8a+88)                    =a(a+11)-8(a+11)                    =(a-8)(a+11)
Q u e s t i o n : 1 5 0
Factorize each of the following algebraic expression:
a
2
 - 14a - 51
S o l u t i o n :
To factorise a2-14a-51, we will find two numbers p and q such that p+q=-14 and pq=-51.Now, 3+(-17)=-14 and 3×(-17)=-51Splitting the middle term -14a in the given quadratic as 3a-17a, we
a2-14a-51=a2+3a-17a-51                       =(a2+3a)-(17a+51)                       =a(a+3)-17(a+3)                       =(a-17)(a+3)
Q u e s t i o n : 1 5 1
Factorize each of the following algebraic expression:
x
2
 + 14x + 45
S o l u t i o n :
To factorise x2+14x+45, we will find two numbers p and q such that p+q=14 and pq=45.Now, 9+5=14 and 9×5=45Splitting the middle term 14x in the given quadratic as 9x+5x, we get:x2+
                      =(x2+9x)+(5x+45)                      =x(x+9)+5(x+9)                      =(x+5)(x+9)
Q u e s t i o n : 1 5 2
Factorize each of the following algebraic expression:
x
2
 - 22x + 120
S o l u t i o n :
To factorise x2-22x+120, we will find two numbers p and q such that p+q=-22 and pq=120.Now, (-12)+(-10)=-22 and (-12)×(-10)=120Splitting the middle term -22x in the given quadratic as -
x2-22x+12=x2-12x-10x+120                      =(x2-12x)+(-10x+120)                      =x(x-12)-10(x-12)                      =(x-10)(x-12)
Q u e s t i o n : 1 5 3
Factorize each of the following algebraic expression:
x
2
 - 11x - 42
S o l u t i o n :
To factorise x2-11x-42, we will find two numbers p and q such that p+q=-11 and pq=-42.Now,3+(-14)=-22 and 3×(-14)=42Splitting the middle term -11x in the given quadratic as-14x+3x, we
 x2-11x-42=x2-14x+3x-42                       =(x2-14x)+(3x-42)                       =x(x-14)+3(x-14)                       =(x+3)(x-14)
Q u e s t i o n : 1 5 4
Factorize each of the following algebraic expression:
a
2
 + 2a - 3
S o l u t i o n :
To factorise a2+2a-3, we will find two numbers p and q such that p+q=2 and pq=-3.Now, 3+(-1)=2 and  3×(-1)=-3Splitting the middle term 2a in the given quadratic as-a+3a, we get:a2+2a-3=
                  =(a2-a)+(3a-3)                  =a(a-1)+3(a-1)                  =(a+3)(a-1)
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Q u e s t i o n : 1 4 7
Factorize each of the following algebraic expression:
x
2
 + 12x - 45
S o l u t i o n :
To factorise x2+12x-45, we will find two numbers p and q such that p+q=12 and pq=-45.Now, 15+(-3)=12 and 15×(-3)=-45Splitting the middle term 12x in the given quadratic as -3x+15x, we
 x2+12x-45=x2-3x+15x-45                       =(x2-3x)+(15x-45)                       =x(x-3)+15(x-3)                       =(x+15)(x-3)
Q u e s t i o n : 1 4 8
Factorize each of the following algebraic expression:
40 + 3x - x
2
S o l u t i o n :
We have:40+3x-x2 ?-(x2-3x-40) To factorise (x2-3x-40), we will find two numbers p and q such that p+q=-3 and pq=-40.Now,  5+(-8)=-3 and 5×(-8)=-40Splitting the middle term -3x in the given
40+3x-x2=-(x2-3x-40)                    =-(x2+5x-8x-40)                    =-[(x2+5x)-(8x+40)]                    =-[x(x+5)-8(x+5)]                    =-(x-8)(x+5)                    =(x+5)(-x+8)
Q u e s t i o n : 1 4 9
Factorize each of the following algebraic expression:
a
2
 + 3a - 88
S o l u t i o n :
To factorise a2+3a-88, we will find two numbers p and q such that p+q=3 and pq=-88.Now,  11+(-8)=3 and 11×(-8)=-88Splitting the middle term 3a in the given quadratic as 11a-8a, we get:a
                    =(a2+11a)-(8a+88)                    =a(a+11)-8(a+11)                    =(a-8)(a+11)
Q u e s t i o n : 1 5 0
Factorize each of the following algebraic expression:
a
2
 - 14a - 51
S o l u t i o n :
To factorise a2-14a-51, we will find two numbers p and q such that p+q=-14 and pq=-51.Now, 3+(-17)=-14 and 3×(-17)=-51Splitting the middle term -14a in the given quadratic as 3a-17a, we
a2-14a-51=a2+3a-17a-51                       =(a2+3a)-(17a+51)                       =a(a+3)-17(a+3)                       =(a-17)(a+3)
Q u e s t i o n : 1 5 1
Factorize each of the following algebraic expression:
x
2
 + 14x + 45
S o l u t i o n :
To factorise x2+14x+45, we will find two numbers p and q such that p+q=14 and pq=45.Now, 9+5=14 and 9×5=45Splitting the middle term 14x in the given quadratic as 9x+5x, we get:x2+
                      =(x2+9x)+(5x+45)                      =x(x+9)+5(x+9)                      =(x+5)(x+9)
Q u e s t i o n : 1 5 2
Factorize each of the following algebraic expression:
x
2
 - 22x + 120
S o l u t i o n :
To factorise x2-22x+120, we will find two numbers p and q such that p+q=-22 and pq=120.Now, (-12)+(-10)=-22 and (-12)×(-10)=120Splitting the middle term -22x in the given quadratic as -
x2-22x+12=x2-12x-10x+120                      =(x2-12x)+(-10x+120)                      =x(x-12)-10(x-12)                      =(x-10)(x-12)
Q u e s t i o n : 1 5 3
Factorize each of the following algebraic expression:
x
2
 - 11x - 42
S o l u t i o n :
To factorise x2-11x-42, we will find two numbers p and q such that p+q=-11 and pq=-42.Now,3+(-14)=-22 and 3×(-14)=42Splitting the middle term -11x in the given quadratic as-14x+3x, we
 x2-11x-42=x2-14x+3x-42                       =(x2-14x)+(3x-42)                       =x(x-14)+3(x-14)                       =(x+3)(x-14)
Q u e s t i o n : 1 5 4
Factorize each of the following algebraic expression:
a
2
 + 2a - 3
S o l u t i o n :
To factorise a2+2a-3, we will find two numbers p and q such that p+q=2 and pq=-3.Now, 3+(-1)=2 and  3×(-1)=-3Splitting the middle term 2a in the given quadratic as-a+3a, we get:a2+2a-3=
                  =(a2-a)+(3a-3)                  =a(a-1)+3(a-1)                  =(a+3)(a-1)
Q u e s t i o n : 1 5 5
Factorize each of the following algebraic expression:
a
2
 + 14a + 48
S o l u t i o n :
To factorise a2+14a+48, we will find two numbers p and q such that p+q=14 and pq=48.Now, 8+6=14 and 8×6=48Splitting the middle term 14a in the given quadratic as 8a+6a, we get:a2+
                       =(a2+8a)+(6a+48)                       =a(a+8)+6(a+8)                       =(a+6)(a+8)
Q u e s t i o n : 1 5 6
Factorize each of the following algebraic expression:
x
2
 - 4x - 21
S o l u t i o n :
To factorise x2-4x-21, we will find two numbers p and q such that p+q=-4 and pq=-21.Now,3+(-7)=-4 and 3×(-7)=-21Splitting the middle term -4x in the given quadratic as -7x+3x, we get:x2-
                    =(x2-7x)+(3x-21)                    =x(x-7)+3(x-7)                    =(x+3)(x-7)
Q u e s t i o n : 1 5 7
Factorize each of the following algebraic expression:
y
2
 + 5y - 36
S o l u t i o n :
To factorise y2+5y-36, we will find two numbers p and q such that p+q=5 and pq=-36.Now, 9+(-4)=5 and 9×(-4)=-36Splitting the middle term 5y in the given quadratic as -4y+9y, we get: y2+
                     =(y2-4y)+(9y-36)                     =y(y-4)+9(y-4)                     =(y+9)(y-4)
Q u e s t i o n : 1 5 8
Factorize each of the following algebraic expression:
(a
2
 - 5a)
2
 - 36
S o l u t i o n :
(a2-5a)2-36=(a2-5a)2-62=[(a2-5a)-6][(a2-5a)+6]=(a2-5a-6)(a2-5a+6)In order to factorise a2-5a-6, we will find two numbers p and q such that p+q=-5 and pq=-6Now, (-6)+1=-5 and (-6)×1=-6Spli
a2-5a-6=a2-6a+a-6                   =(a2-6a)+(a-6)                   =a(a-6)+(a-6)                   =(a+1)(a-6)Now,In order to factorise a2-5a+6, we will find two numbers p and q such that p+q=-5 and pq=6C
(-2)+(-3)=-5 and (-2)×(-3)=6Splitting the middle term -5 in the given quadratic as -2a-3a, we get:a2-5a+6=a2-2a-3a+6                   =(a2-2a)-(3a-6)                   =a(a-2)-3(a-2)                   =(a-3)(a-2
? (a2-5a-6)(a2-5a+6)=(a-6)(a+1)(a-3)(a-2)                                                =(a+1)(a-2)(a-3)(a-6)
Q u e s t i o n : 1 5 9
Factorize each of the following algebraic expression:
(a + 7)(a - 10) + 16
S o l u t i o n :
(a+7)(a-10)+16=a2-10a+7a-70+16=a2-3a-54To factorise a2-3a-54 , we will find two numbers p and q such that p+q=-3 and pq=-54.Now, 6+(-9)=-3 and 6×(-9)=-54Splitting the middle term -3a
 a2-3a-54=a2-9a+6a-54                      =(a2-9a)+(6a-54)                      =a(a-9)+6(a-9)                      =(a+6)(a-9)