Question

use the synthetic division and the remainder theorem to find P(a)

Answer 1

$950$

1) Let's begin with the Synthetic Division of that Polynomial by one binomial. This one is

$\begin{gathered} a=-4\Rightarrow(a+4)=0 \\ \\ x+4 \end{gathered}$

This is based on the Factor Theorem.

2) The Remainder Theorem states that:

3) So now, let's divide it with the synthetic division that Polynomial by (x+4)

4) So, applying the Remainder theorem, we can tell that

$P(a)=P(-4)=950$