Question

Find the remainder when $p\left(x\right)=3x^3-4x^2+10x-7$ is divided by $x-2$

• A. $21$
• B. $-21$
• C. $22$
• D. $-22$

Answer 1

Answer: (A)

$21$

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 $a=2$

Hence the remainder is $p\left(2\right)$

$\Rightarrow p\left(2\right)=3(2{)}^3-4(2{)}^2+10\left(2\right)-7=21$

remainder is $21$