Question

question
factor completely.
$3x^2 + 7x + 4$

Explanation:

Step1: Split middle term

Find two numbers that multiply to $3\times4=12$ and add to $7$. These numbers are $3$ and $4$. Rewrite the middle term:
$3x^2 + 3x + 4x + 4$

Step2: Group and factor pairs

Group the first two and last two terms, then factor out GCF from each group:
$3x(x + 1) + 4(x + 1)$

Step3: Factor out common binomial

Factor out the shared binomial $(x+1)$:
$(3x + 4)(x + 1)$

Answer:

$(3x + 4)(x + 1)$