Question

if one factor of $x^2 + 2x - 24$ is $(x+6)$, what is the other factor?\
\\(\bigcirc\\) $(x+8)$\
\\(\bigcirc\\) $(x-8)$\
\\(\bigcirc\\) $(x+4)$\
\\(\bigcirc\\) $(x-4)$

Explanation:

Step1: Set up division

Divide $x^2 + 2x - 24$ by $(x+6)$.

Step2: Divide leading terms

$\frac{x^2}{x} = x$. Multiply $(x+6)$ by $x$: $x^2 + 6x$.

Step3: Subtract from dividend

$(x^2 + 2x - 24) - (x^2 + 6x) = -4x - 24$.

Step4: Divide new leading terms

$\frac{-4x}{x} = -4$. Multiply $(x+6)$ by $-4$: $-4x -24$.

Step5: Subtract to find remainder

$(-4x -24) - (-4x -24) = 0$.

Answer:

D. (x-4)