Question

factor the trinomial:
$3x^2 + 23x + 14$
answer attempt 1 out of 2

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(3\times14 = 42\) and add up to \(23\). The numbers are \(21\) and \(2\) since \(21\times2 = 42\) and \(21 + 2=23\).

Step2: Rewrite the middle term

Rewrite \(23x\) as \(21x+2x\) in the trinomial: \(3x^{2}+21x + 2x+14\).

Step3: Group and factor

Group the first two terms and the last two terms: \((3x^{2}+21x)+(2x + 14)\). Factor out the greatest common factor from each group: \(3x(x + 7)+2(x + 7)\).

Step4: Factor out the common binomial

Factor out the common binomial \((x + 7)\): \((3x + 2)(x + 7)\).

Answer:

\((3x + 2)(x + 7)\)