Question

1. factor the trinomial.

$3x^2 + 20x + 12$
$3x^2 + 20x + 12 = \square$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(3\times12 = 36\) and add up to \(20\). The numbers are \(2\) and \(18\) since \(2\times18 = 36\) and \(2 + 18 = 20\).

Step2: Split the middle term

Rewrite the middle term \(20x\) using \(2\) and \(18\):
\(3x^{2}+18x + 2x+12\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((3x^{2}+18x)+(2x + 12)\)
Factor out the greatest common factor from each group:
\(3x(x + 6)+2(x + 6)\)

Step4: Factor out the common binomial

Now, factor out the common binomial \((x + 6)\):
\((3x + 2)(x + 6)\)

Answer:

\((3x + 2)(x + 6)\)