Question

question
factor completely.
$2x^2 + 19x + 9$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(2\times9 = 18\) and add up to \(19\). The numbers are \(18\) and \(1\) since \(18\times1=18\) and \(18 + 1=19\).

Step2: Split the middle term

Rewrite the middle term \(19x\) as \(18x+x\):
\(2x^{2}+18x + x+9\)

Step3: Group the terms

Group the first two terms and the last two terms:
\((2x^{2}+18x)+(x + 9)\)

Step4: Factor out the GCF from each group

Factor out \(2x\) from the first group and \(1\) from the second group:
\(2x(x + 9)+1(x + 9)\)

Step5: Factor out the common binomial factor

Factor out \((x + 9)\):
\((2x + 1)(x + 9)\)

Answer:

\((2x + 1)(x + 9)\)