Question

Using remainder theorem, find the remainder when $2x^3-3x^2+4x-5$ is divided by $x+3$.

• A. $204$
• B. $-136$
• C. $-98$
• D. $42$

Answer 1

Answer: (C)

$-98$

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

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

$\Rightarrow p(-3)=2(-3{)}^3-3(-3{)}^2+4(-3)-5$

$\Rightarrow p(-3)=-98$