Question

name:date:review for eoc exam - part 15. marisol is working with the functions$h(x) = x^3 - 4x^2 - x + 4$and$j(x) = x + 1$.she needs to determine whether or not $j(x)$ is a factor of $h(x)$, so she divides the functions. complete her statement below based on the results of the division.$j(x)$ select one:• $square$ is• $square$ is nota factor of $h(x)$ because $\frac{h(x)}{j(x)}$ has:• $square$ a zero remainder• $square$ a non-zero remainder

Explanation:

Step1: Apply Factor Theorem

For $j(x)=x+1$, find root: $x=-1$. Evaluate $h(-1)$:
$h(-1) = (-1)^3 - 4(-1)^2 - (-1) + 4$

Step2: Calculate $h(-1)$

$h(-1) = -1 - 4(1) + 1 + 4 = -1 -4 +1 +4 = 0$

Step3: Interpret result

A remainder of 0 means $j(x)$ is a factor.

Answer:

$j(x)$ $\boldsymbol{\text{is}}$ a factor of $h(x)$ because $\frac{h(x)}{j(x)}$ has: $\boldsymbol{\text{a zero remainder}}$