Question

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

Answer 1

The other factor is (x+3)

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

$(x + 3)$