Factoring Trinomials by the Trial and Error Method (when the coefficient of
the 1st term is a 1)
1. Always factor out the greatest common factor first!
If the first term is a negative also factor out a (¨C1) as this will make the
factoring process easier.
(Note: At this point the coefficient in front of the first term should be a 1.
If the coefficient in front of the first term is not a 1 then the following
steps do not apply.)
2. Setting up your first terms!
After factoring out the common factor, the trinomial will factor into two
binomials as shown below if it is factorable.
(First term + Last term)(First term + Last term)
The first terms multiplied together should equal the first term of the
trinomial.
3. Getting the signs right !
If the last term of the trinomial is positive then the signs will be the same as
the middle term either both positive or both negative. If the last term of the
trinomial is negative then the signs will be different, one positive and one
negative.
4. Last terms: Trial and Error!
The product of the last terms always multiply together to give you the last term
of the trinomial. The sum of the product of the inside terms and the product of
the outside terms should add together to give you the middle term of the
trinomial. (Note: Be sure to include the signs of the last terms when
multiplying and adding)
Example 1: x² - 9x + 20
There is no common factor so we begin by setting up the first terms as follows:
(x )(x )
Next we get the signs right . Since the last term is positive, the signs will be
the same as the middle term which is negative .
(x - )(x - )
Finally we determine the last terms by trial and error. The last terms
multiplied together should equal 20 and when added together equal ¨C9. Therefore
our last terms will be ¨C4 and ¨C5.
(x - 4)(x - 5)
Example 2: x² - x - 20
Again there is no common factor so we begin by setting up our first terms as
follows:
(x )(x )
the signs right. Since the last term is negative, one term will be
positive and the other will be negative.
(x - )(x + )
Finally we determine the last term by trial and error. The terms multiplied
together must equal ¨C20 and when added together equal ¨C1. Therefore our last
terms will be ¨C5 and 4.
(x - 5)(x + 4)
