Question

What is the remainder if we divide $6x^3+x^2-2x+4$ by
($x-2$)?

Answer 1

According to the remainder theorem, if p(x) be any polynomial of degree greater than or equal to one and let “a” be any real number, if p(x) is divided by (x-a), then the remainder is p(a).

The Polynomial

$p\left(x\right)=6x^3+x^2-2x+4$ and $g\left(x\right)=x-2.$

We have to find the value of p(2).

So by remainder theorem

$p\left(2\right)=6(2{)}^3+(2{)}^2-2\left(2\right)+4$

$=6\left(8\right)+4-4+4$

$=48+4$

= 52.

Hence, when $6x^3+x^2-2x+4$ is divided by $x-2$ we get $52$ as remainder.