Question

using remainder theorem find the reminder when x^3-6x^2+2x-4 divided by (-2x+1)​

Answer 1

Here, g(x)=3x−1. To apply Remainder theorem, (3x−1) should be converted to (x−a) form.

∴3x−1= 1/3(3x-1) =x− 1/3

∴g(x)=(x− 1/3)

By remainder theorem, r(x)=p(a)=p( 1/3)

p(x)=x³ −6x² +2x−4

⇒p(1/3)=( 1/3)³-6( 1/3)²+2(1/3)-4

= (1/27) - 6/9+2/3-4

=(1-18+18-108)/27

=-107/27

∴ the remainder p(1/3)=-107/27