Polynomials Lesson 4: Factoring Polynomials Using Decomposition
Todays Objectives:
 Students will be able to demonstrate an understanding of common factors and
trinomial factoring, including:
 Model the factoring of a trinomial, concretely or pictorially, and record
the process symbolically
 Generalize and explain strategies used to factor a trinomial
 Express a polynomial as a product of its factors
Vocabulary: Factoring by decomposition
 A method of factoring when the middle term (𝑏) of a trinomial, 𝑎𝑥 2 + 𝑏𝑥 + 𝑐, is
written as a sum of 2 terms, then finding a common factor between the two pairs
of terms formed.
Factoring by Decomposition
In this lesson, you will learn how to ______ polynomials of the form ______________,
where the leading coefficient (a) is not 1, nor does it become 1 by factoring out a
_________ __________ __________
Look at the polynomial 2x3 + 13 x + 15.
Here, a = __, b = ___, c = ___.
Step 1) ____________ a andc to find a product that will be used to break apart b, or
“____________” b.
So,
Step 2) Now find any two _________ of 30 that when _______, equal b, or 13.
*Remember that negative numbers may be factors too.
In this case, two factors that add to 13 are ___ and ___: 3+10=13; (3)(10)=30.
Step 3) Now, _________ _______ (decompose) the middle term, b, into two _____
_________, using the two factors just found (3 and 10).
So, 2x2 + 13x + 15 now becomes _____________________
*it doesn’t matter the order of the terms.
Step 4) Find the ___________ __________ between the first two terms (____ + ____) as
well as the last two terms (____ + ___), and factor them out.
 For this example, the common factor of the first two terms is ____, and the
common factor of the last two terms is ___

 Notice that both brackets are ______________ (the same)
Step 5) Put the two factored out terms into one pair of brackets (___ + ____), and take
one of the identical binomials (___+ ___) and rewrite the expression like this: (___+
___)(___ +___)
You have now factored the polynomial.
*To test if you are right, multiply your answer to see if you get the original trinomial
(2x2 + 13x + 15).
Example 1)(You do) Factor 8p2 – 18p - 5
Example 2)(You do) Factor 6x2 – 21x + 9
Homework: pg. 177-178 #5, 7, 10, 13-16, 18-20