Question

factor completely. w^2 + 19w - 20

Explanation:

Step1: Find two numbers

We need two numbers that multiply to -20 and add up to 19. The numbers are 20 and - 1 since \(20\times(-1)=-20\) and \(20+( - 1)=19\).

Step2: Rewrite the middle - term

Rewrite \(w^{2}+19w - 20\) as \(w^{2}+20w - w - 20\).

Step3: Group the terms

Group the terms: \((w^{2}+20w)-(w + 20)\).

Step4: Factor out the GCF from each group

Factor out \(w\) from the first group and - 1 from the second group: \(w(w + 20)-1(w + 20)\).

Step5: Factor out the common binomial factor

Factor out \((w + 20)\): \((w + 20)(w-1)\).

Answer:

\((w + 20)(w - 1)\)