Question

The remainder when $x^2-2x+7$ is divided by $x+4$ is:

• A. $28$
• B. $29$
• C. $30$
• D. $31$

Answer 1

The correct option is D $31$

Let $f\left(x\right)=x^2-2x+7$.

The polynomial $f\left(x\right)$ is divided by $x+4$.

Then $x+4=0⟹x=-4.$
By remainder theorem, the remainder is given by $f(-4)$.
Hence, remainder of the given polynomial $f\left(x\right)$ is
$f(-4)=(-4{)}^2-2(-4)+7=16+8+7=31$.
That is, the remainder obtained is $31$.

Hence, option $D$ is correct.