x^2 - 5x - 24
Since it's asking us to factorize this, no order of operations is needed.
We can't factor the equation in it's current form, so we need to see if it's possible to split the middle term.
List factors of -24.
1 * -24
-1 * 24
2 * -12
-2 * 12
3 * -8 (these factors fit the criteria and can be used to split the middle term.)
x^2 + 3x - 8x - 24
Factor each binomial.
x(x + 3) - 8(x + 3)
(x - 8)(x + 3) is the fully factored form of the trinomial.