Question

On dividing x3
-3x2+x+2 by a polynomial g(x), the quotient and remainder
were x-2 and -2x+4 respectively. Find g(x).

Answer 1

Answer:

Given

f(x)=x

3

+5x

2

−ax+6

Let us assume

x−1=0⇒x=1

By remainder theorem, when f(x) is divide by (x−1),

Remainder r=f(1)

⇒2a=(1)

3

+5(1)

2

−a(1)+6[∵r=2a(Given)]

⇒2a=1+5−a+6

⇒2a+a=12

⇒3a=12

⇒a=

3

12

⇒a=4

Therefore, the value of a is 4.