Question

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

Answer 1

`(x+3)(x+5)`

Explanation:

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

Answer 2

`(x+5)(x+3)`

Explanation:

Do it backwards to double check.

FOIL

First: x times x is `x^2`
Outer: x times 3 is `3x`
Inner: x times 5 is `5x`
Last: 5 times 3 is `15`

Add like terms: `x^2` + `(3x + 5x)` + `15`

Final answer: `x^2` + `8x` + `15`