FACTORING REVIEW

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FACTORING REVIEW

• Math 0099
• Chapter 6
• Created and Presented by
• Laura Ralston

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STEP 1

• Always check to see if you have a Greatest
  Common Factor (GCF). If so, remove it from the
  problem first.
• The GCF is a number, letter, or combination
  thereof in each term of the problem.
• If the leading coefficient is negative, factor
  out a -1

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STEP 2

• Depends on the number of terms the polynomial
  contains
• A) If the polynomial has 2 terms, check to see if
  it is a difference of two squares by asking
  yourself three questions.

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THE QUESTIONS

• Is the first term squared?
• Is the second term squared?
• Is there a minus sign between terms?
• You must answer YES to all three to proceed.

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Difference of Two Squares

• a2 - b2 (a b) (a - b)

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STEP 2 , Part B)

• If you have 4 terms, you will use grouping
  technique.
• Break the problem into 2 smaller problems by
  considering the first two terms as one and the
  second two terms as another.
• Look for GCF in each pair. Once you have removed
  the GCF from each pair, the expression in the
  parentheses should be the same. It is now the
  GCF.

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STEP 2, Part C)

• If you have 3 terms, rewrite the polynomial with
  4 terms and use the grouping technique (ac
  method) or trial and error technique
• For ac method
• Multiply the coefficient on the squared term and
  the constant.
• List the pairs of numbers that will give you
  that product

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Continued..

• Using the sign in front of the constant, decide
  which pair will give you the coefficient on the
  middle term.
• Rewrite and use grouping technique by replacing
  the middle term with the pair you selected.

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STEP 3

• As a final check, see if any of the factors you
  have written can be factored further. If you
  have overlooked a common factor, you can catch
  it here.
• Rule of thumb exponents on variable will most
  often be 1.

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STEP 4

• If nothing will factor, the polynomial is PRIME.
  
• Move on to the next problem

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Examples

• 1) a2 4a 3

• 2) y2 8y 15

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Examples

• 3) x2 3x - 10

• 4) m2 m - 6

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Examples

• 5) y2 - 49

• 6) 49x2 4

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Examples

• 7) -2y2 24y - 70

• 8) 3n3 15n2 18n

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Examples

• 9) 14 11x 15x2

• 10) 252x 175x3

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Examples

• 11) 2xz 10x z 5

• 12) 2x3 14x2 3x 21

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Assignment

• Page 479 1-65 odd