Question

factor the expression.
$3x^2 + 23x + 14$
$3x^2 + 23x + 14 = \square$
(type your answer in factored form.)

Explanation:

Step1: Find pair for AC method

Multiply $3 \times 14 = 42$. Find two numbers that multiply to 42 and add to 23: 21 and 2.

Step2: Split middle term

Rewrite $23x$ as $21x + 2x$:
$3x^2 + 21x + 2x + 14$

Step3: Factor by grouping

Group first/last two terms:
$(3x^2 + 21x) + (2x + 14)$
Factor GCF from each group:
$3x(x + 7) + 2(x + 7)$

Step4: Factor common binomial

Factor out $(x + 7)$:
$(3x + 2)(x + 7)$

Answer:

$(3x + 2)(x + 7)$