Question

The remainder when $7x^3+5x^2-7x-11$ is divided by $x-0.5$ is?

Answer 1

Given: $7x^3+5x^2-7x-11$ is divided by $(x-0.5)$.

The remainder theorem states that when you divide a polynomial $f\left(x\right)$ by a linear factor $(x-a)$, you will have a quotient function $q\left(x\right)$ and a remainder.

The remainder $=f\left(a\right)$. This remainder can be found using long division, synthetic division or the remainder theorem.

Using Remainder Theorem:

Linear factor $(x-a)=(x-0.5)$

This means $a=0.5$.

We have $f\left(x\right)=7x^3+5x^2-7x-11$

Hence, $f\left(0.5\right)=7(0.5{)}^3+5(0.5{)}^2-7\left(0.5\right)-11$

$=0.875+1.25-3.5-11$

$=-12.375$

Hence, the required remainder is $-12.375$.