if one factor of $x^{2}+2x - 24$ is $(x + 6)$, what is the other factor?\n$(x + 8)$\n$(x - 8)$\n$(x +…

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

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

Answer

Explanation:

Step1: Set up the factoring

Let (x^{2}+2x - 24=(x + 6)(x+a)). Expand the right - hand side: ((x + 6)(x+a)=x^{2}+ax+6x + 6a=x^{2}+(a + 6)x+6a).

Step2: Equate coefficients

We have the equation (x^{2}+2x - 24=x^{2}+(a + 6)x+6a). Equate the coefficient of (x): (a + 6=2), so (a=2 - 6=-4). Also, equate the constant terms: (6a=-24), which gives (a=\frac{-24}{6}=-4).

Answer:

D. ((x - 4))