RD Sharma (Very Short Answer Questions): Factorization of Polynomials

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Q u e s t i o n : 7 1
Define zero or root of a polynomial.
S o l u t i o n :
A real number a is a zero
orroot of the polynomial f(x), if f (a) = 0
Q u e s t i o n : 7 2
If x =
1
2
is a zero of the polynomial fx
= 8x
3
 + ax
2
 - 4x + 2, find the value of a.
S o l u t i o n :
Since is a zero of polynomial f(x).
Therefore 
Page 2


 
  
     
 
 
  
       
        
    
   
      
 
  
     
 
 
  
       
Q u e s t i o n : 7 1
Define zero or root of a polynomial.
S o l u t i o n :
A real number a is a zero
orroot of the polynomial f(x), if f (a) = 0
Q u e s t i o n : 7 2
If x =
1
2
is a zero of the polynomial fx
= 8x
3
 + ax
2
 - 4x + 2, find the value of a.
S o l u t i o n :
Since is a zero of polynomial f(x).
Therefore 
The value of a is .
Q u e s t i o n : 7 3
Write the remainder when the polynomial f(x) = x
3
 + x
2
 - 3x + 2 is divided by x + 1.
S o l u t i o n :
When the polynomial f(x), divided by the remainder will be
Thus, the reminder = 5
Q u e s t i o n : 7 4
Find the remainder when x
3
 + 4x
2
 + 4x - 3  is divided by x.
S o l u t i o n :
When the polynomial f(x) = x
3
 + 4x
2
 + 4x - 3 is divided by x the remainder will be.
Thus, the reminder = -3
Q u e s t i o n : 7 5
If x + 1 is a factor of x
3
 + a, then write the value of a.
S o l u t i o n :
As is a factor of polynomial 
i.e. 
(-1)
3
+a = 0 ? a = 1
Thus, the value of a = 1
Q u e s t i o n : 7 6
If f(x) = x
4
 - 2x
3
 + 3x
2
 - ax - b when divided by x - 1, the remainder is 6, then find the value of a + b
S o l u t i o n :
When polynomial  divided by 
The remainder is 6.
i.e. 
Thus, the value of