What is the remainder when $(x^3 - 2x^2 + 5x - 6) div(x - 3)$ ?

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Answer 1 · 2018-06-12T06:39:15

The remainder is $=18$

Apply the remainder theorem :

When the polynomial $f(x)$ is divided by $(x-c)$ , then

$f(x)=(x-c)q(x)+r(x)$

And when $x=c$

$f(c)=0*q(x)+r=r$

where $r$ is the remainder

Here,

$f(x)=x^3-2x^2+5x-6$

and

$c=3$

Therefore,

$f(3)=27-18+15-6=18$

The remainder is $=18$

What is the remainder when (x^3 - 2x^2 + 5x - 6) div(x - 3)(x^3 - 2x^2 + 5x - 6) div(x - 3)?