There are two different types of trinomials that we are going to learn how to factor over the next two lessons. The first type is when we have a leading coefficient of one, and the second trinomial we are going to factor is when there is a leading coefficient other than one.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
So let’s start by learning how to factor a trinomial with a leading coefficient of 1.
First, we must ensure that our trinomial is in standard form, where we write each term in order of decreasing degree.
Once this is complete, we are ready for easy to follow steps for factoring trinomials when a=1:
- Set up two blank parentheses.
- If the last term is positive, then both parentheses take the sign of the middle term. If the last term is negative, then the parentheses have opposite signs.
- List all the factors of the constant term and choose the pair that adds to make the middle term.
- Place these factors in the parentheses and check by multiplying.
Standard Form of a Quadratic Trinomial
The coolest thing is that we will be creating two binomials that when multiplied together yield our given trinomial.
We must always keep in mind that factoring is the reverse of multiplying, as the Math Page so nicely reminds us. And that is why we can always check our answers by FOILing!
Factoring trinomials can be challenging at first since we are using a “guess and check” method.
But, the more you practice, the easier it becomes.
Together we are going to look at all different types of trinomials, including perfect square trinomials, and practice not only pulling out the GCF but our new skills of how to factor a trinomial with a leading coefficient of one.
Trinomial Coefficient One – Video
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