nial: 3x^{2}+13x + 4

$nial: 3x^{2}+13x + 4$

Multiply the coefficient of $x^{2}$ (3) and the constant term (4), $3\times4 = 12$.

Find two numbers that multiply to 12 and add up to 13. The numbers are 12 and 1 since $12\times1=12$ and $12 + 1=13$.

Rewrite the middle - term $13x$ as $12x+x$. So, $3x^{2}+13x + 4=3x^{2}+12x+x + 4$.

Group the terms: $(3x^{2}+12x)+(x + 4)$.

Factor out the common factors from each group. From $3x^{2}+12x$, we get $3x(x + 4)$, and from $x + 4$, it remains as is. So, $3x(x + 4)+1(x + 4)$.

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

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