Question

factor.
$3x^2 + 32x + 20$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(3\times20 = 60\) and add up to \(32\). The numbers are \(30\) and \(2\) since \(30\times2 = 60\) and \(30 + 2 = 32\).

Step2: Rewrite the middle term

Rewrite the quadratic as \(3x^{2}+30x + 2x+20\).

Step3: Group and factor

Group the first two terms and the last two terms: \((3x^{2}+30x)+(2x + 20)\). Factor out the greatest common factor from each group: \(3x(x + 10)+2(x + 10)\).

Step4: Factor out the common binomial

Factor out \((x + 10)\) to get \((3x + 2)(x + 10)\).

Answer:

\((3x + 2)(x + 10)\)