Question

25. Factorise the following polynomial using synthetic division : 2x3 - 3x2 - 3x + 2​

Answer 1

Answer:

Let f(x)=2x

3

+3x

2

−9x−10, then f(−1)=−2+3+9−10=0

So, by remainder theorem, when f(x) is divided by x+1, the remainder is 0. So, (x+1) is a factor of f(x)

f(2)=16+12−18−10=0

So, by similar reasoning, (x−2) is also a factor of f(x)

Therefore, f(x)=(x+1)(x−2)p(x)=(x

2

−x−2)p(x)

By synthetic division, we can find p(x)

⇒f(x)=2x

3

+3x

2

−9x−10=(x

2

−x−2)(2x+5)

Therefore p(x)=2x+5 and the factorization of f(x) is

f(x)=(x+1)(x−2)(2x+5)