Question

factor completely.
11w² - 13w + 2

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(11\times2 = 22\) and add up to \(- 13\). The numbers are \(-11\) and \(-2\) since \((-11)\times(-2)=22\) and \(-11 + (-2)=-13\).

Step2: Rewrite the middle term

Rewrite \(-13w\) as \(-11w-2w\) in the expression \(11w^{2}-13w + 2\), so we get \(11w^{2}-11w-2w + 2\).

Step3: Group the terms

Group the first two terms and the last two terms: \((11w^{2}-11w)+(-2w + 2)\).

Step4: Factor out the GCF from each group

Factor out \(11w\) from the first group: \(11w(w - 1)\), and factor out \(-2\) from the second group: \(-2(w - 1)\). Now the expression becomes \(11w(w - 1)-2(w - 1)\).

Step5: Factor out the common binomial factor

Factor out \((w - 1)\) from both terms: \((11w - 2)(w - 1)\).

Answer:

\((11w - 2)(w - 1)\)