7.2 Factoring Using the Distributive Property

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7.2 Factoring Using the Distributive Property

• CORD Math
• Mrs. Spitz
• Fall 2006

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Objectives

• Use the GCF and the distributive property to
  factor polynomials.
• Use the information you are gaining now to get
  into Algebra II next year or test Math 121, so
  you can get into a decent college next year.

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Assignment

• Pg. 263 4-35 all

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Introduction

• In chapter 6, you multiplied a polynomial by a
  monomial by using the distributive property. You
  can also reverse the process and express a
  polynomial in factored form by using the
  distributive property.

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Yeah, so what does that mean?

• Multiplying Polynomials

• Factoring polynomials

The expression 3y(4x 2) at the right above is
not considered fully factored since the
polynomial 4x 2 can be factored as 2(2x 1).
The completely factored form of 12xy and 6y would
be 6y(2x 1). Factoring a polynomial or finding
the factored form of a polynomial means to find
its completely factored form.
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Ex. 1 Use the distributive property to factor
10y2 15y

• First, find the greatest common factor for 10y2
  and 15y

• Then, express each term as the product of the GCF
  and its remaining factors.

The GCF is 5y.
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Ex. 2 Factor 21ab2 33a2bc

• First, find the greatest common factor for 21ab2
  and 33a2bc

• Then, express each term as the product of the GCF
  and its remaining factors.

The GCF is 3ab.
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Ex. 3 Factor 6x3y2 14x2y 2x2

• First, find the greatest common factor for 6x3y2
  and 14x2y and 2x2

• Then, express each term as the product of the GCF
  and its remaining factors.

The GCF is 2x2.