question\nfactor.\n$x^{2}-5x - 14$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to - 14 and add up to - 5. The numbers are - 7 and 2 since $(-7)\times2=-14$ and $-7 + 2=-5$.

Step2: Rewrite the middle - term

Rewrite $-5x$ as $-7x+2x$. So, $x^{2}-5x - 14=x^{2}-7x + 2x-14$.

Step3: Group the terms

Group the terms: $(x^{2}-7x)+(2x - 14)$.

Step4: Factor out the GCF from each group

Factor out the greatest common factor (GCF) from each group. From $x^{2}-7x$, the GCF is $x$, so we get $x(x - 7)$. From $2x-14$, the GCF is 2, so we get $2(x - 7)$.

Step5: Factor out the common binomial factor

Factor out the common binomial factor $(x - 7)$: $x(x - 7)+2(x - 7)=(x - 7)(x + 2)$.

Answer:

$(x - 7)(x + 2)$