Factoring by Grouping

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Factoring by Grouping
Objective After completing this section,
students should be able to factor polynomials by
grouping.
After completing these notes, you will be ready
to do the following assignments.
Assignment 6.6 Worksheet p. 282 1-19
odd
Standard CA 11.0 Factor polynomials by grouping.
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Steps for factoring by grouping
1. A polynomial must have 4 terms to factor by
grouping.
2. We factor the first two terms and the second
two terms separately. Use the rules for GCF to
factor these.
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Examples
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Examples
You must always check to see if the expression is
factored completely. This expression can still
be factored using the rules for difference of two
squares. (see 6.2)
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Examples
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Try These Factor by grouping.
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Solutions
If you did not get these answers, click the green
button next to the solution to see it worked out.
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BACK
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When you factor a negative out of a positive, you
will get a negative.
BACK
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Now factor the difference of squares.
BACK
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BACK
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Factor by Grouping

• Goal To be able to factor polynomials with 4
  terms by grouping

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When

• When does it work? Always
• When should I use it? For any polynomial but
  especially when you have 4 or more terms.

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Steps

1. Put ( ) around first 2 terms and last 2 terms
2. Factor out a common factor so what is left in the
   binomials is the same
3. Make the numbers you factored out into a binomial
   and multiply it by 1 of the same binomials

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Factoring by Grouping

• Use when there are 4 Terms
• 6x3 9x2 4x - 6

3x2(2x 3)
2(2x 3)
(2x 3)
( 3x2 2)
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Factoring by Grouping

• Use when there are 4 Terms
• x3 x2 x 1

x2( x 1)
1( x 1)
(x 1)
( x2 1)
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Factoring by Grouping

• Use when there are 4 Terms
• x3 2x2 - x - 2

-
x2( x 2)
1( x 2)
(x 2)
( x2 - 1)
( x - 1)(x 1)
(x 2)
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Factor completely if possible8x3 2x2 12x 3
(4x 1)(2x2 3)
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Factor completely if possible4x3 - 6x2 - 6x 9
(2x - 3)(2x2 - 3)
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Factor completely if possible4x3 - 6x2 - 6x 9
(2x - 3)(2x2 - 3)