Page 116 - Math Course 2 (Book 1)

Factoring: Polynomials

Mo. 4

Lesson 1

ax + bx + ay + by
KEY CONCEPTS: = x(a + b) + y(a + b)
1. Factor polynomials by using the = (a + b)(x + y)
Distributive Property.
2. Solve quadratic equations of the form Factoring Grouping
2
3
ax2 + bx = 0. Factor: 2x + 6x – 3x – 9
2
3
2x + 6x – 3x – 9
MO. 4 - L1a
The Distributive Property: 2x + 6x 2 – 3x – 9
3
Factoring Polynomials

2
Vocabulary A-Z 2x (x + 3) –3(x + 3)
Let us learn some vocabulary 2x (x + 3) –3(x + 3)
2

ab – cb = b(a – c)

Factoring
2
(x + 3)(2x – 3)
Factoring a polynomial means to f nd its completely
factored form.

Distributive Property to multiply a polynomial by a
monomial. Concept Summary
2a + (6a + 8) = 2a (6a) + 2a(8)
= 12a + 16a Factoring by Grouping
2
Words A polynomial can be factored by grouping
You can reverse this process to express a if all of the following situations exist.
polynomial as the product of a monomial factor
and a polynomial factor. • There are four more terms.
12a + 16a = 2a (6a) + 2a(8) • Terms with common factors can be
2
= 2a + (6a + 8) grouped together.
• The two common factors are identical or
are additive inverses of each other.
2
Thus, a factored form of 12a + 16a is 2a(6a+8)
Symbols ax + bx + ay + by = x(a + b) + y(a + b)
= (a + b) (x + y)
Factoring by grouping

Using the Distributive Property to factor polynomials
having four or more terms is called factoring by
grouping.

Pairs of terms are grouped together and factored.
The Distributive Property is then used a second time
to factor a common binomial factor.

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