Question

question
factor completely.
$3x^2 + 5x + 2$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(3\times2 = 6\) and add up to \(5\). The numbers are \(2\) and \(3\) since \(2\times3 = 6\) and \(2 + 3=5\).

Step2: Rewrite the middle term

Rewrite \(5x\) as \(2x+3x\) in the expression \(3x^{2}+5x + 2\), so we get \(3x^{2}+2x+3x + 2\).

Step3: Group the terms

Group the first two terms and the last two terms: \((3x^{2}+2x)+(3x + 2)\).

Step4: Factor out the GCF from each group

Factor out \(x\) from the first group: \(x(3x + 2)\), and factor out \(1\) from the second group: \(1(3x + 2)\). Now the expression becomes \(x(3x + 2)+1(3x + 2)\).

Step5: Factor out the common binomial factor

Factor out \((3x + 2)\) from both terms: \((3x + 2)(x + 1)\).

Answer:

\((3x + 2)(x + 1)\)