# How do you factor the trinomial x²+8x+15?

Apr 13, 2018

$\left(x + 3\right) \left(x + 5\right)$

#### Explanation:

First, find the factors of 15.
$15 = 1 \cdot 15 = 3 \cdot 5$
Now, split 8x into 2 terms of "x"s containing the numbers 1 and 15 or 3 and 5.
$x + 15 x \ne 8 x$, but $3 x + 5 x = 8 x$
Now we have ${x}^{2} + 3 x + 5 x + 15$.
Next factor x from ${x}^{2}$ and $3 x$.
$x \left(x + 3\right)$
Also factor 5 from $5 x$ and $15$.
$5 \left(x + 3\right)$
We can notice that $x \left(x + 3\right)$ and $5 \left(x + 3\right)$ both contain $\left(x + 3\right)$. Since they both also multiply we can say that the answer is $\left(x + 3\right) \left(x + 5\right)$.

Apr 13, 2018

$\left(x + 5\right) \left(x + 3\right)$

#### Explanation:

Do it backwards to double check.

FOIL

First: x times x is ${x}^{2}$
Outer: x times 3 is $3 x$
Inner: x times 5 is $5 x$
Last: 5 times 3 is $15$

Add like terms: ${x}^{2}$ + $\left(3 x + 5 x\right)$ + $15$

Final answer: ${x}^{2}$ + $8 x$ + $15$