MATD 0390 Intermediate Algebra
Section 4.4: Introduction to Factoring
Christy Dittmar
Introduction to Factoring (4.4)
Greatest Common Factor (GCF)
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Find the GCF of the coefficients.
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Include the smallest power of every variable in the polynomial.
8x 4 y ! 4x 2 y 2
If the first term is negative, the GCF should be negative also.
!6x 2 yz 2 + 11x 2 y 2 z
Factor. 5x 2 yz ! 10xyz 2 + 30x 2 z 2
Common Binomial Factor
Factor out the common binomial ( a ! 1) the same way you factor out the GCF.
x ( a ! 1) + 2 ( a ! 1)
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MATD 0390 Intermediate Algebra
Section 4.4: Introduction to Factoring
Christy Dittmar
Factoring by Grouping (4 term polynomials)
•
Group the polynomial by first terms and last terms
•
Factor out the GCF of each group
•
Factor out the common binomial, if there is one
If there is not a common binomial in the last step, then the polynomial cannot be factored by this
method. Check your steps, and make sure the terms are arranged in descending powers before
determining this.
2x 3 + 10x 2 + 3x + 15
3x 3 ! 7 + 3x ! 7x 2
16t 3 ! 8st 2 ! 6st + 3s 2
2x 3 ! 3x 2 ! 4x ! 6
First step in ANY factoring problem: factor out GCF, if there is one.
15t 4 + 18t 3 ! 5t 2 ! 6t
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