Polynomials Lesson 1: Common Factors of a Polynomial
Todays Objectives:
 Students will be able to demonstrate an understanding of common factors and
trinomial factoring, including:
o Determine the common factors in the terms of a polynomial, and express
the polynomial in factored form
o Model the factoring of a trinomial, and record the process symbolically
Vocabulary Words:
_____________ - One term or the sum of terms whose variables have whole number
exponents
_____________ - a polynomial with one term; examples) 14, 3x, -2x2
_____________ – a polynomial with two terms; examples) 3x + 2, 6x2 - 3
_____________ – a polynomial with three terms; example) x2 + 4x – 8
____________________ -diagrams used to represent polynomial expressions
____________________- diagrams which use rectangles to describe polynomials
In today’s lesson we will learn to use tools called __________ ________ that can be
used to represent polynomial expressions. We will use 6 different algebra tiles:
1) small squares – represents “1 or-1” (depending on color), side length of 1, area = 1
2) rectangles – represents “x or -x”, length of x, width of 1, area = x
3) large squares – represents “x2 or –x2”, side length of x, area = x2
Example) How can we represent the binomial 4x + 12 using algebra tiles?
Solution: there are several different ways that we can represent this binomial. Find all
the possible ways that you can create a __________ out of the tiles for the binomial 4x +
12: (4 rectangles, 12 small squares)
1(4x + 12) = 4x + 12
Representation:
___________________
Representation:
___________________
Representation:
The diagrams above show that there are _______ ways to factor the expression 4m + 12.
The first two ways we say are _____________ because they can both be factored
further. The third way we say is ___________ because the GCF of 4m and 12 is 4.
Example) Factor the binomial 6n + 9 using algebra tiles
Solution:
The dimensions of the rectangle are：
Example)(You do) Factor the binomial 6c + 4c2using algebra tiles and by finding the GCF
Solution:Algebra Tiles:
Solution:Find the GCF
The GCF is ＿＿. Write each term as a product of 2c and another polynomial.
When a polynomial has negative terms or ＿ different terms, we cannot remove a
common factor by arranging the tiles as a rectangle. Instead, we can sometimes arrange
the tiles into ________ ________.
Example) Factoring Trinomials
Factor the trinomial 5 – 10z – 5z2. Verify that the factors are correct.
Solution:
To factor a trinomial using algebra tiles, we arrange the tiles into equal groups instead of
trying to make rectangles.
There are ___ equal groups and each group contains the trinomial 1 – 2z – z2.
So, the factors are ___ and __________
Another method is finding the GCF of the each term of the trinomial:
Example)(You do) Factor the trinomial. Verify that the factors are correct.
-12x3y – 20xy2 – 16x2y2
Solution:
Homework:

Pg. 155-156 # 4, 7, 9, 11, 14-18