Question

The binomial (x 5) is a factor of x2 8x 15. what is the other factor?

Answer 1

the answer is (x+3)

Explanation:

on edge

Answer 2

We can do this in two different ways:

Method 1
Since

`(x + 5)`
is a factor, we can use it to obtain the other factor by long division(see attachment).

`{x}^(2) + 8x + 15 = (x + 5)(x + 3)`


Hence the other factor is

`(x + 3)`

Method 2

We can factor the trinomial to obtain the other factor.

Two factors of 15 that add up to 8 are,


`5,3`
We split the middle term as follows:

`{x}^(2) + 8x + 15 = {x}^(2) + 3x + 5x + 15`

`{x}^(2) + 8x + 15 = x(x + 3) + 5(x + 3)`

`{x}^(2) + 8x + 15 = (x + 3) (x + 5)`
Hence the other factor is


`(x + 3)`