Question

factor the trinomial: $3x^{2}+13x+4$

Explanation:

Step1: Identify $a,b,c$ for $ax^2+bx+c$

$a=3$, $b=13$, $c=4$

Step2: Find two terms with product $ac$, sum $b$

$ac=3\times4=12$; terms $12$ and $1$ (since $12+1=13$)

Step3: Split middle term and group

$3x^2 + 12x + x + 4 = 3x(x+4) + 1(x+4)$

Step4: Factor out common binomial

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

Answer:

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