Question

practice factoring trinomials with a leading coefficient of 1 and a positive constant term. the binomial (x + 5) is a factor of x^2 + 8x + 15. what is the other factor? (x + 3) (x + 7) (x + 12) (x + 13)

Explanation:

Step1: Recall factoring trinomial formula

For a trinomial $ax^{2}+bx + c$ (here $a = 1$), if $(x + m)$ is a factor and the trinomial is $x^{2}+bx + c$, we know that $x^{2}+bx + c=(x + m)(x + n)=x^{2}+(m + n)x+mn$. Given one factor $(x + 5)$ of $x^{2}+8x + 15$, we have $m = 5$, $b=8$, $c = 15$.

Step2: Find the other factor

We know that $mn=15$ and $m = 5$, so $n=\frac{15}{5}=3$. Also, $m + n=8$ (since the coefficient of $x$ in $x^{2}+8x + 15$ is 8 and $m = 5$, then $5 + n=8$ gives $n = 3$). So the other factor is $(x + 3)$.

Answer:

A. $(x + 3)$