March 12, 2015
- 1. Today's Goals: Introduction to Factoring the GCF 03/12/15 Review for Test: Polynomial Operations Document: Test Review/Notes Continuing Concepts: New Concepts: Expanding Binomials/Factoring Trinomials
- 2. Find the area of the triangle: x2 + 1 2x - 4 x3 - 2x2 + x - 2 Test Review: bh 2 10y2 + 7y + 64ft.
- 3. Test Review: (2a2 b + b2 )2 Expanding Binomials: Factoring Trinomials: (8x3 - 18x) Common Factors? 2x(4x2 - 9) Factor Complete? 2x(2x+3)(2x - 3) Which brings us to today's topic: Factoring the GCF
- 5. Factoring the GCF: We'll start by distributing the monomial Starting with the coefficients, and then the variables, is there anything all three terms have in common? If so, factor it out, then determine what is left. The point of factoring is to simplify 1) 3x(2x2 – 3x + 4) Factor: 2) 14x3y + 7x2y – 7xy = 6x3 – 9x2 + 12x = 7xy(2x2 + x – 1)
- 6. Factors: Quantities that are multiplied together to form a product. 3 • 4 = 12 Factors Product An algebra example: (x + 2)(x + 3) = Factors Product x2 + 5x + 6 There are several methods that can be used when factoring polynomials. The method used depends on the type of polynomial that you are factoring. We will spend the next few weeks learning to factor by: 1. Greatest Common Factor 2. Grouping 3. Difference of Squares 4. Sum or Difference of Cubes 5. Special Case Trinomials Factoring Polynomials
- 7. ** Remember that the method of factoring depends on the type of polynomial being factored. Throughout this process, pay attention not only on how to factor, but the type of polynomial being factored. As we progress, you will have to correctly match the factoring method with the polynomial. Factoring Polynomials Greatest Common Factor: GCF Pros: -- simple to understand Cons: -- most polynomials cannot be completly factored this way Factoring Method #1 Whole numbers that are multiplied together to find a product are called factors of that product. A number is divisible by its factors. 2•2 •3 =12
- 8. When factoring polynomials, the first step is to ALWAYS look for a GCF. If so, it is factored out. The remaining polynomial may or may not be able to be simplified further using other methods. Prime factorization is used to make sure you have the GCF. Factoring Polynomials Example 1: Writing Prime Factorizations Write the prime factorization of 98. Factor tree Method Choose any two factors of 98 to begin. Keep finding factors until each branch ends in a prime factor. 98 = 2 7 7 The prime factorization of 98 is 2 7 7 or 2 7298 2 49 7 7
- 9. Simplify by finding the GCF (26x3y2 z3)(52xy4z2) = The GCF of 26 and 52 is 26xy2z2 Factoring the GCF: (2) 213 xxxyyzzz 2213 xyyyyzz The simplified product is 26xy2z2(2x2y2z)
- 10. Handout: The one document you can use with your test Each version of the test will have a problem from the handout on it. You can submit your completed document with your test for extra credit.