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March 6 March 6 Presentation Transcript

  • March 6, 2013 Today: Review all Factoring Methods CoveredTest Grades Posted Today: V6MathQuarter Grades Posted Tomorrow: V6MathNew Factor Method: Difference of Squares New Khan Academy Topics(2) for 3/10/13 Class Work
  • This is a good time to step back, Take a deep breath.. (Quietly)And review what weve covered thus far in the factoring unit.
  • Greatest Common FactorExample: Find the GCF of each list of numbers. 1) 6, 8 and 46 6=2·3 8=2·2·2 46 = 2 · 23 So the GCF is 2. 2) 144, 256 and 300 144 = 2 · 2 · 2 · 3 · 3 256 = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 300 = 2 · 2 · 3 · 5 · 5 So the GCF is 2 · 2 = 4.
  • Greatest Common FactorExample: Find the GCF of each list of terms. 1) x3 and x7 x3 = x · x · x x7 = x · x · x · x · x · x · x So the GCF is x · x · x = x3 2) 6x5 and 4x3 6x5 = 2 · 3 · x · x · x 4x3 = 2 · 2 · x · x · x So the GCF is 2 · x · x · x = 2x3
  • Greatest Common FactorExample: Find the GCF of the following list of terms. a3b2, a2b5 and a4b7 a3b2 = a · a · a · b · b a2b5 = a · a · b · b · b · b · b a4b7 = a · a · a · a · b · b · b · b · b · b · b So the GCF is a · a · b · b = a2b2Notice that the GCF of terms containing variableswill use the smallest exponent found amongst theindividual terms for each variable.
  • Factor Using GCF Most factoring using GCF is done with binomials. Factor using GCF: 1. 32x3 – 4x2 2. 18x2y + 5xy2Sometimes, factoring using GCF is just the first step. 3. 18x2 – 50 4. x3 – 49x
  • factor by Grouping When a polynomial has 4 or more terms, grouping is the factor method used.Factor: xy + 2x + y + 2 It should be clear that we need to rearrange the terms since there is nothing that can be factored from the 3rd & 4th terms. (xy + y) + (2x + 2) = y(x + 1) + 2(x + 1) = (x + 1)(y + 2)
  • factor by Grouping1. xy – 4x + 3y - 122. 2xy - 6x - y + 33. 2x3 – x2 – 10x + 54. 2x + 18 – 9y – xy
  • Factoring: x 2 + bx + cFactor c, using those factors whose sum equals b 1. x2 – 2x – 35 3. x2 + 5x + 1 2. x2 – 7x + 10 4. x2 + x - 2
  • Factoring ax2 + bx + c trinomialsFirst, multiply ac, then, factor c using those factorswhose sum is equivalent to b. Finally, use groupingto factor the trinomial 1. 2x2 + 7x + 6 3. 3x2 + 17x + 1 2. 3x2 + 14x - 5 4. 8x2 + 2x - 3 5. 6x2 + 7x - 3
  • Solving Equations by FactoringZero Factor Theorem • If a and b are real numbers and ab = 0, then a = 0 or b = 0.1. x2 + 6x + 8 = 0 3. 6x2 - 14x = -8 x = -4, x = -2 x = 1, x = 11/32. x2 - 25 = 0 4. 4x2 - 4x = 24 x = 5, x = -5 x = -2, x = 3
  • Difference of Two SquaresAnother shortcut for factoring a trinomial is whenwe want to factor the difference of two squares. a2 – b2 = (a + b)(a – b) A binomial is the difference of two squares if: 1.Both terms are squares and 2.The signs of the terms are different. 9x2 – 25y2 – c4 + d4
  • Difference of Two Squares1. b2 - 49 3. 1 - 16x10 =(b- 7)(b+ 7) (1 - 4x5)(1 + 4x5)2. 7g3h2 - 28g5 = 4. x2y2 - 25 = 7g3(h2 - 4g2) = (xy - 5)(xy + 5) 7g3(h - 2g)(h + 2g) 5. 144 - x8 = (12 - x4)(12 + x4)