Question

factor completely.
2q² - 7q - 9

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(2\times(-9)= -18\) and add up to \(-7\). The numbers are \(-9\) and \(2\) since \(-9\times2 = -18\) and \(-9 + 2=-7\).

Step2: Rewrite the middle term

Rewrite \(-7q\) as \(-9q + 2q\) in the expression: \(2q^{2}-9q + 2q-9\).

Step3: Group and factor

Group the first two terms and the last two terms: \((2q^{2}-9q)+(2q - 9)\). Factor out the greatest common factor from each group: \(q(2q - 9)+1(2q - 9)\). Now factor out the common binomial factor \((2q - 9)\): \((q + 1)(2q - 9)\).

Answer:

\((q + 1)(2q - 9)\)