Question

Let $p\left(x\right)=x^4-3x^2+2x+5$. Find the remainder when $p\left(x\right)$ is divided by $(x-1)$.

Answer 1

We know that the remainder when a polynomial $p\left(x\right)$ is divided by $(x-a)$ is $p\left(a\right)$.

Given that,

$p\left(x\right)=x^4-3x^2+2x+5$

Divisor $=(x-1)$

So, The Remainder $=p\left(1\right)$

$=(1{)}^4-3(1{)}^2+2\left(1\right)+5$

$=1-3+2+5$

$=5$