Question

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

• A. $197$
• B. $113$
• C. $-1$
• D. $0$

Answer 1

The correct option is B $113$

Remainder Theorem states that the remainder of the division of a polynomial $f\left(x\right)$ by a linear polynomial $(x-a)$ is $f\left(a\right)$ or in other words $(x-a)$ is divisor of $f\left(x\right)$ if and only if $f\left(a\right)=0$

Here $a=3$

Let $p\left(x\right)=4x^3+5x-10$

remainder is when you put $x=3$ in $p\left(x\right)=p\left(3\right)$

$p\left(x\right)=4\times 3^3+5\times 3-10$

$\Rightarrow p\left(3\right)=113$