EDGE Math 8

Factoring Other Trinomials

Trinomials in the Form $a x^{2} + b x + c$

(Continuation from the previous slide)

Since the trinomial you are factoring is $2 x^{2} + x - 15,$ you have to find the combination of binomial factors for which the sum of the outside and inside terms (the O and I in FOIL) will be equal to the middle term (x) of the trinomial. The computation of the O and I for all possible binomial factors are shown below.

Notice that the combination $(2 x - 5) (x + 3)$ gives the desired sum of x for the outside and inside terms. Thus, the given trinomial can be factored as

2 x^{2} + x - 15 = (2 x - 5) (x + 3) .