Question

if $x - 9$ is a factor of $x^2 - 5x - 36$, what is the other factor?\
$\bigcirc$ $x - 4$\
$\bigcirc$ $x + 4$\
$\bigcirc$ $x - 6$\
$\bigcirc$ $x + 6$

Explanation:

Step1: Set up factor form

Let the other factor be $x+a$. Then $(x-9)(x+a)=x^2-5x-36$.

Step2: Expand left-hand side

$x^2+(a-9)x-9a = x^2-5x-36$

Step3: Match constant terms

$-9a=-36$
Solve for $a$: $a=\frac{-36}{-9}=4$

Step4: Verify linear coefficient

Check $a-9=4-9=-5$, which matches the coefficient of $x$ in the original quadratic.

Answer:

B. $x+4$