Question

Using remainder theorem, find the remainder when $3x^2+x+7$ is divided by $x+2$

• A. $17$
• B. $-23$
• C. $13$
• D. $-29$

Answer 1

The correct option is A $17$

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 $a=-2$

Let $p\left(x\right)=3x^2+x+7$

Remainder is when you put $x=-2$ in $p\left(x\right)$ i.e. $p(-2)$

$p(-2)=3(-2{)}^2+(-2)+7$

$=17$

$\Rightarrow p(-2)=17$