Factoring Trinomials

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The following diagram shows how to factor trinomials with no guessing. Scroll down the page for more examples and solutions of factoring trinomials.
Factor Trinomials

To factor a trinomial means to write the trinomial as a product of two factors. It is the reverse of expansion (FOIL).


In order to factor the trinomial,

Text Box: x2 + bx + c

we need to find two constants p and q such that:

Text Box: x2 + bx + c  =  (x + p)(x + q)

Now, if we expand the RHS we will get:

Text Box: x2 + bx + c  =  (x + p)(x + q)  	        = 	x2 + qx + px + pq  	        =  x2 + (p + q)x + pq

Comparing coefficients, we get:

Reverse FOIL

So, b = p + q and c = pq.

In other words, we need to find two constants p and q such that their sum p + q = b and their product pq = c.

The following videos will illustrate how to factor trinomials.
Factoring Trinomials - with no guessing

Factoring Trinomials - with guessing

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