Question

factor completely.
$2u^2 - 5u - 7$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(2\times(-7)= -14\) 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 \(-5u\) as \(-7u + 2u\) in the expression \(2u^{2}-5u - 7\):
\(2u^{2}-7u + 2u-7\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((2u^{2}-7u)+(2u - 7)\)
Factor out the greatest common factor from each group:
\(u(2u - 7)+1(2u - 7)\)

Step4: Factor out the common binomial

Factor out \((2u - 7)\) from both terms:
\((2u - 7)(u + 1)\)

Answer:

\((2u - 7)(u + 1)\)