Question

Find the remainder in the following cases, when f(x) is divided by g(x) in each case without long division method:. f(x) = 2x ^ 3 - 3x ^ 2 + 7x - 8 , g(x) = x - 1​

Answer 1

Question :

Find the remainder in the following cases, when f(x) is divided by g(x) in each case without long division method:. f(x) = 2x ^ 3 - 3x ^ 2 + 7x - 8 , g(x) = x - 1

Given Equation :

f(x) = 2x ^ 3 - 3x ^ 2 + 7x - 8 , g(x) = x - 1

Solution :

Given,

f(x)=2x³ −3x²+7x−8

Let us assume

x−1=0

⇒x=1

∴ By remainder theorem,

when f(x) is divided by (x−1)

Remainder r=f(1)

=2(1)³−3(1)²+7(1)8

=2−3+7−8

=9−11

=−2

$\small\purple { \: Remainder: =2 }$