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# March 6

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### Transcript of "March 6"

1. 1. 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
2. 2. This is a good time to step back, Take a deep breath.. (Quietly)And review what weve covered thus far in the factoring unit.
3. 3. 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.
4. 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
5. 5. 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.
6. 6. 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
7. 7. 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)
8. 8. factor by Grouping1. xy – 4x + 3y - 122. 2xy - 6x - y + 33. 2x3 – x2 – 10x + 54. 2x + 18 – 9y – xy
9. 9. 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
10. 10. 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
11. 11. 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
12. 12. 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
13. 13. 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)
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