Question

question factor completely. 2x^2 - 5x - 7

Explanation:

Step1: Multiply leading and constant terms

Multiply the coefficient of $x^{2}$ (which is 2) and the constant term (which is - 7). So, $2\times(-7)=-14$.

Step2: Find two - numbers that multiply to - 14 and add to - 5

The two numbers are - 7 and 2 since $(-7)\times2=-14$ and $-7 + 2=-5$.

Step3: Rewrite the middle term

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

Step4: Group the terms

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

Step5: Factor out the greatest common factor from each group

From the first group $2x^{2}-7x$, the GCF is $x$, so $2x^{2}-7x=x(2x - 7)$. From the second group $2x - 7$, the GCF is 1. So, $(2x^{2}-7x)+(2x - 7)=x(2x - 7)+1(2x - 7)$.

Step6: Factor out the common binomial factor

Factor out the common binomial factor $(2x - 7)$. We get $(2x - 7)(x + 1)$.

Answer:

$(2x - 7)(x + 1)$