Find the remainder when $2x^3+3x^2-8x+2$ is divided by $x-2$ (by Remainder theorom)

Given:

$2x^3+3x^2-8x+2$ is divided by $x-2$

To do:

Use remainder theorem to find the remainder when $2x^3+3x^2-8x+2$ is divided by $x-2$.

Solution:

The remainder theorem states that when a polynomial, $p(x)$ is divided by a linear polynomial, $x - a$ the remainder of that division will be equivalent to $p(a)$.

$f(x) = 2x^3 + 3x^2 - 8x+2$

$g(x) = x -2$

So, the remainder will be $f(2)$.

$f(2) = 2(2)^3+3(2)^2-8(2) + 2$

$= 2(8) + 3(4) -16+2$

$=16+12-14$

$=14$

Therefore, the remainder is $14$. 

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Updated on: 10-Oct-2022

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