Question

How do you factor the expression d² + 2d - 15?

Answer 1

You use the sum-product method, based on the expression:
`(x+a)(x+b)=x^2+(a+b)x+(a*b)`

Explanation:

First you factor `15`. This can be done in only two ways:
`15=1*15=3*5` (not looking at the signs yet).
Since the sum or difference between `1and15` are too great, we go for the second option.

Then you notice that the `15` has a `-`sign. This means that the factors have opposite signs, and we are looking for the difference between these signs.
So this could be `(-3and +5) or (+3and-5)`

Since the second term has a `+`sign it must be the first:

`=(x-3)(x+5)`