Question

What is the remainder of the expression, show all necessary steps.

Answer 1

Explanation

We are asked to find the remainder when

$\frac{5x^3+7x+5}{x+2}$

To do so, we can use the remainder theorem

The remainder theorem states that the remainder when p(x) is divided by (x - a) is p(a).

So in our case

$p(x)=5x^3+7x+5$

$\begin{gathered} (x-a)=x+2 \\ where \\ a=-2 \end{gathered}$

So we will substitute -2 into p(x) to get the remainder

$5(-2)^3+7(-2)+5=5(-8)+7(-2)+5=-40-14+5=-49$

Therefore, the remainder is -49