Question

Find the remainder when $x^3+4x^2-7x+6$ is divided by $x-1.$

• A. $4$
• B. $1$
• C. $3$
• D. $2$

Answer 1

The correct option is A $4$

Let $f\left(x\right)=x^3+4x^2-7x+6$

According to remainder theorem, if a polynomial $f\left(x\right)$ is divided by a linear function $x-k$, then the remainder is $f\left(k\right)$.

The remainder when $f\left(x\right)$ is divided by $x-1$ is
$f\left(1\right)=1^3+4(1{)}^2-7+6=4$