Factor each completely $$ \times \quad n^{2}+13 n+40 $$

Question

UpStudy AI · Accepted Answer

We start with the quadratic

$$
n^2 + 13n + 40.
$$

**Step 1.** Identify two numbers $$ r $$ and $$ s $$ such that

$$
r \times s = 40 \quad \text{and} \quad r + s = 13.
$$

**Step 2.** The pair $$ 5 $$ and $$ 8 $$ satisfies these conditions since

$$
5 \times 8 = 40 \quad \text{and} \quad 5 + 8 = 13.
$$

**Step 3.** Write the factored form using these numbers:

$$
n^2 + 13n + 40 = (n + 5)(n + 8).
$$
$$ n^2 + 13n + 40 = (n + 5)(n + 8) $$

Factor each completely \[ \times \quad n^{2}+13 n+40 \]