Question

How do you factor a trinomial? Please help.

Answer 1

FACTORING IS THE REVERSE of multiplying. Skill in factoring, then, depends upon skill in multiplying.

As for a quadratic trinomial:

2x² + 9x − 5

it will be factored as a product of binomials:

(? ?)(? ?)

The first term of each binomial will be the factors of 2x², and the second term will be the factors of 5. Now, how can we produce 2x²? There is only one way: 2x· x :

(2x ?)(x ?)

And how can we produce 5? Again, there is only one way: 1· 5. But does the 5 go with 2x --

(2x 5)(x 1)

or with x

(2x 1)(x 5) ?

Notice: We have not yet placed any signs

How shall we decide between these two possibilities? It is the combination that will correctly give the middle term, 9x :

2x² + 9x − 5.

Consider the first possibility:

(2x 5)(x 1)

Is it possible to produce 9x by combining the outers and the inners: 2x· 1 with 5· x ?

No, it is not. Therefore, we must eliminate that possibility and consider the other:

(2x 1)(x 5)

Can we produce 9x by combining 10x with x ?

Yes if we choose +5 and −1:

(2x − 1)(x + 5)

(2x − 1)(x + 5) = 2x² + 9x − 5.