Question

select the correct answer from each drop - down menu.
consider this polynomial, where a is an unknown real number.
$p(x)=x^{4}+5x^{3}+ax^{2}-3x + 11$
the remainder of the quotient of $p(x)$, and $(x + 1)$ is 17.
braulio uses synthetic division to find the value of a, and zahra uses the remainder theorem to find the value of a. their work is shown.
braulio
$\begin{array}{r|rrrrr}1&1&5&a&-3&11\\&&1&6&a + 6&a + 3\hline&1&6&a + 6&a + 3&a + 14end{array}$
$a + 14 = 17$
$a = 3$
zahra
$p(-1)=(-1)^{4}+5(-1)^{3}+a(-1)^{2}-3(-1)+11$
$=-1 + 5 - a + 3 + 11$
$=a + 18$
$p(-1)=17$
$a + 18 = 17$
$a=-1$
braulio 🔘 found the value of a because he 🔘.
zahra 🔘 found the value of a because she 🔘.

Explanation:

Answer:

made an error in synthetic division (used \(x = 1\) instead of \(x=-1\)), used the correct formula \(p(-1)\) for the remainder theorem