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6.4 Factoring and Solving Polynomial Equations

6.4 Factoring and Solving Polynomial Equations. Factoring Sum or Difference of Cubes. If you have as sum or difference of cubes such as a 3 +b 3 or a 3 –b 3 , you can factor by using the following patterns. Note: The first and last term are cubed and these are binomials. Example.

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6.4 Factoring and Solving Polynomial Equations

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  1. 6.4 Factoring and Solving Polynomial Equations

  2. Factoring Sum or Difference of Cubes If you have as sum or difference of cubes such as a3 +b3 or a3 –b3, you can factor by using the following patterns. Note: The first and last term are cubed and these are binomials.

  3. Example Factor x3 + 343. Note: This is a binomial. Are the first and last terms cubed? S O P x3 + 343 = (x)3 + (7)3 = ( + )( - + ) x 7 x2 7x 49

  4. Example Factor 64a4 – 27a = a(64a3 – 27) Note: Binomial. Is the first and last terms cubes? = a( (4a)3 – (3)3) Note: = a( - )( + + ) 4a 3 16a2 12a 9 S O P

  5. Factor by Grouping Some four term polynomials can be factor by grouping. Example. Factor 3x3 + 7x2 +12x + 28 Step 1 Pair the terms. Step 2 Factor out common factor from each pair. Identical factors Step 3 Factor out common factor from each term.

  6. Example Factor 3x3 + 7x2 -12x - 28 Step 1 Note: Subtraction is the same as adding a negative Step 2 Step 3 Note: This factor can be further factored

  7. Solving Polynomial Equations Solve Set equation equal to zero. Factor. Set each factor equal to zero and solve.

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