question\nfactor.\n$x^{2}+2x - 24$

Explanation:

Step1: Identify coefficient and constant

We have the quadratic $x^{2}+2x - 24$, where the coefficient of $x^{2}$ is 1, the coefficient of $x$ is 2 and the constant is -24.

Step2: Find two numbers

We need two numbers that multiply to -24 and add up to 2. The numbers are 6 and -4 since $6\times(-4)=-24$ and $6+( - 4)=2$.

Step3: Rewrite the middle - term

Rewrite $x^{2}+2x - 24$ as $x^{2}+6x-4x - 24$.

Step4: Group the terms

Group the terms: $(x^{2}+6x)-(4x + 24)$.

Step5: Factor out the GCF from each group

Factor out the GCF from each group: $x(x + 6)-4(x + 6)$.

Step6: Factor out the common binomial

Factor out the common binomial $(x + 6)$ to get $(x + 6)(x-4)$.

Answer:

$(x + 6)(x - 4)$