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Factoring polynomials

T
toukie19

The document discusses two methods for factoring polynomials: 1. Factoring polynomials with a common monomial factor by finding the greatest common factor (GCF) and dividing the polynomial by the GCF. 2. Factoring polynomials that are a difference of squares by applying the rule that a2 - b2 = (a + b)(a - b). It provides an example of each method and cites image sources used under Creative Commons licenses.

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Factoring a polynomial means expressing it as a product of other polynomials.
Factoring Method #1 Factoring polynomials with a common monomial factor (Using GCF) **Always look for a GCF before using any other factoring method.**
Steps: 1. Find the greatest common factor. 2. Divide the polynomial by the GCF. The quotient is the other factor. 3. Express the polynomial as the product of the quotient and the GCF.
3 2 2 Example : 6c d 12c d 3cd Step 1: GCF 3cd Step 2: Divide by GCF 3 2 2 (6c d 12c d 3cd) 3cd 2 2c 4cd 1
The answer should look like this: 3 2 2 Ex: 6c d 12c d 3cd 2 3cd(2c 4cd 1)
Factoring Method #2 Factoring polynomials that are a difference of squares.
Apply the rule... 2 2 a b (a b)(a b) 2 Ex: x 16 2 2 x 4 (x 4)(x 4)
Citations Animal Number 1," 息 2010 horse50, used under a Creative Commons Attribution-ShareAlike license: http://openclipart.org/people/horse50/one.svg Mathematician," 息 2006 NASA / johnny_automatic used under a Creative Commons Attribution-ShareAlike license: http://openclipart.org/people/johnny_automatic/johnny_automatic_mathematician.svg

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Factoring polynomials

  • 2. Factoring a polynomial means expressing it as a product of other polynomials.
  • 3. Factoring Method #1 Factoring polynomials with a common monomial factor (Using GCF) **Always look for a GCF before using any other factoring method.**
  • 4. Steps: 1. Find the greatest common factor. 2. Divide the polynomial by the GCF. The quotient is the other factor. 3. Express the polynomial as the product of the quotient and the GCF.
  • 5. 3 2 2 Example : 6c d 12c d 3cd Step 1: GCF 3cd Step 2: Divide by GCF 3 2 2 (6c d 12c d 3cd) 3cd 2 2c 4cd 1
  • 6. The answer should look like this: 3 2 2 Ex: 6c d 12c d 3cd 2 3cd(2c 4cd 1)
  • 7. Factoring Method #2 Factoring polynomials that are a difference of squares.
  • 8. Apply the rule... 2 2 a b (a b)(a b) 2 Ex: x 16 2 2 x 4 (x 4)(x 4)
  • 9. Citations Animal Number 1," 息 2010 horse50, used under a Creative Commons Attribution-ShareAlike license: http://openclipart.org/people/horse50/one.svg Mathematician," 息 2006 NASA / johnny_automatic used under a Creative Commons Attribution-ShareAlike license: http://openclipart.org/people/johnny_automatic/johnny_automatic_mathematician.svg