Question

How do you factor completely `x^2 + 10x + 21`?

Answer 1

`x^2+10x+21 = (x+7)(x+3)`

Explanation:

Note that `(x+a)(x+b) = x^2+(a+b)x+ab`

So we want to find a pair of factors of `21` with sum `10`

The pair `7, 3` works, so we find:

`x^2+10x+21 = (x+7)(x+3)`