Question

How do you factor the trinomial `m^2 + 8m + 12`?

Answer 1

`m^2+8m+12 = (m+2)(m+6)`

Explanation:

Notice that `2+6 = 8` and `2 xx 6 = 12`

So: `m^2+8m+12 = (m+2)(m+6)`

In general, we find:

`(m+a)(m+b) = m^2+(a+b)m+ab`

So if you have a monic quadratic (one that has a leading coefficient of `1`) to factor, typically you are looking for a pair of factors of the constant term with sum or difference equal to the middle coefficient.