Question

question
factor completely.
$2x^2 + 9x + 4$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(2\times4 = 8\) and add up to \(9\). The numbers are \(1\) and \(8\) since \(1\times8 = 8\) and \(1 + 8=9\).

Step2: Rewrite the middle term

Rewrite \(9x\) as \(x + 8x\) in the expression \(2x^{2}+9x + 4\):
\[2x^{2}+x + 8x + 4\]

Step3: Group the terms

Group the first two terms and the last two terms:
\[(2x^{2}+x)+(8x + 4)\]

Step4: Factor out the GCF from each group

Factor out \(x\) from the first group and \(4\) from the second group:
\[x(2x + 1)+4(2x + 1)\]

Step5: Factor out the common binomial factor

Factor out \((2x + 1)\) from the two terms:
\[(2x + 1)(x + 4)\]

Answer:

\((2x + 1)(x + 4)\)