Question

factor
$n^2 + 16n + 63$
$(n - 7)(n + 4)$
$(n + 7)(n + 9)$
$(n - 3)(n - 10)$
$(n + 7)(n - 9)$

Explanation:

Step1: Find pair summing to 16, product 63

We need two numbers that add up to 16 and multiply to 63. These numbers are 7 and 9, since $7+9=16$ and $7\times9=63$.

Step2: Factor the quadratic expression

For a quadratic of the form $n^2+bn+c$, it factors to $(n+m)(n+k)$ where $m+k=b$ and $m\times k=c$. Substitute $m=7$, $k=9$.
$n^2 + 16n + 63=(n+7)(n+9)$

Step3: Match with options

Compare the factored form to the given choices.

Answer:

B. (n+7)(n+9)