Question

factor completely.
$2u^2 + 3u - 2$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(2\times(-2) = -4\) and add up to \(3\). The numbers are \(4\) and \(-1\) since \(4\times(-1)=-4\) and \(4 + (-1)=3\).

Step2: Rewrite the middle term

Rewrite \(3u\) as \(4u - u\) in the expression \(2u^{2}+3u - 2\):
\(2u^{2}+4u - u - 2\)

Step3: Group the terms

Group the first two terms and the last two terms:
\((2u^{2}+4u)+(-u - 2)\)

Step4: Factor out the GCF from each group

Factor out \(2u\) from the first group and \(-1\) from the second group:
\(2u(u + 2)-1(u + 2)\)

Step5: Factor out the common binomial factor

Factor out \((u + 2)\) from the two terms:
\((2u - 1)(u + 2)\)

Answer:

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