Question

Using remainder theorem, find the reminder when $4x^3+5x-10$ is divided by $x-3$

• A. $12$
• B. $18$
• C. $96$
• D. $113$

Answer 1

The correct option is D $113$

Let $p\left(x\right)=4x^3+5x-10$ and
$g\left(x\right)=x-3$
$=>x-3=0$
$=>x=3$
The remainder when $p\left(x\right)$ is divided by $g\left(x\right)$ is $p\left(3\right)$ (By Remainder Theorem)
Thus, $p\left(3\right)=4(3{)}^3+5(3)-10$
$=108+15-10$
$=113$
Therefore,
Remainder=$113$