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WARM UP • Write down objective and homework in agenda. • Lay out homework (Faceing Equations worksheet) • Homework (Factor a=1 worksheet) Warm Up • Math 8 benchmark Vocabulary! • Factoring trinomials: Find the binomial factors of trinomials Teach me how to factor… • http://www.youtube.com/watch?v=OFSrINhf NsQ Review: (y + 2)(y + 4) First terms: y2 Outer terms: +4y Inner terms: +2y Last terms: +8 Combine like terms. y2 + 6y + 8 y +2 y2 +2y +4 +4y +8 y In this lesson, we will begin with y2 + 6y + 8 as our problem and finish with (y + 2)(y + 4) as our answer. Here we go! 1) Factor y2 + 6y + 8 Do we have a GCF? Nope! Now we will learn Trinomials! You will set up a table with the following information. Product of the first and last coefficients Middle coefficient The goal is to find two factors in the first column that add up to the middle term in the second column. We’ll work it out in the next few slides. M A 1) Factor y2 + 6y + 8 Create your MAMA table. Product of the first and last coefficients Multiply +8 Add +6 Middle coefficient Here’s your task… What numbers multiply to +8 and add to +6? If you cannot figure it out right away, write the combinations. 1) Factor y2 + 6y + 8 Place the factors in the table. Multiply +8 Which has a sum of +6? +1, +8 -1, -8 +2, +4 -2, -4 Add +6 +9, NO -9, NO +6, YES!! -6, NO We are going to use these numbers in the next step! 1) Factor Multiply +8 +2, +4 2 y + 6y + 8 Add +6 +6, YES!! Hang with me now! Replace the middle number of the trinomial with our working numbers from the MAMA table y2 + 6y + 8 y2 + 2y + 4y + 8 Now, group the first two terms and the last two terms. We have two groups! (y2 + 2y)(+4y + 8) Almost done! Find the GCF of each group and factor it out. If things are done right, the y(y + 2) +4(y + 2) parentheses should Factor out the GCF’s. Write them in their own group. be the same. (y + 4)(y + 2) Tadaaa! There’s your answer…(y + 4)(y + 2) You can check it by multiplying. M A 2) Factor x2 – 2x – 63 Create your MAMA table. Product of the first and last coefficients Signs need to be different since number is negative. Multiply -63 -63, 1 -1, 63 -21, 3 -3, 21 -9, 7 -7, 9 Add -2 -62 62 -18 18 -2 2 Middle coefficient Replace the middle term with our working numbers. x2 – 2x – 63 x2 – 9x + 7x – 63 Group the terms. (x2 – 9x) (+ 7x – 63) Factor out the GCF x(x – 9) +7(x – 9) The parentheses are the same!! (x + 7)(x – 9) Here are some hints to help you choose your factors in the MAMA table. 1) When the last term is positive, the factors will have the same sign as the middle term. 2) When the last term is negative, the factors will have different signs. 2) Factor 2x2 - 14x + 12 Find the GCF! 2(x2 – 7x + 6) Now do the MAMA table! Signs need to be the same as the middle sign since the product is positive. Multiply +6 Add -7 -1, -6 -7 -2, -3 -5 Replace the middle term. 2[x2 – x – 6x + 6] Group the terms. 2[(x2 – x)(– 6x + 6)] Factor out the GCF 2[x(x – 1) -6(x – 1)] The parentheses are the same! 2(x – 6)(x – 1) Don’t forget to always look for a GCF first!! More Examples! • http://www.regentsprep.org/Regents/math/A LGEBRA/AV6/PracFact2.htm Factor x2 + 3x + 2 1. 2. 3. 4. (x + 2)(x + 1) (x – 2)(x + 1) (x + 2)(x – 1) (x – 2)(x – 1) You Try!!! • 1) (x+4)(x+25) • 2) (x−9)(x+3) You Try!!! • 3) (x+4)(x+4) • 4) (x− 5)(x− 4) You Try! • 5) (a+ 4b)(a+ 12b) • 6) (a− 25)(a+ 1) More Practice! • http://www.quia.com/jg/678595.html • http://www.quia.com/jg/678595.html • http://hotmath.com/help/gt/genericalg1/secti on_6_10.html Extra Resources • http://www.phschool.com/webcodes10/index.cfm?fus eaction=home.gotoWebCode&wcprefix=ata&wcsuffix= 0905 • http://www.phschool.com/atschool/academy123/engli sh/academy123_content/wl-book-demo/ph-275s.html • http://teachers.henrico.k12.va.us/math/hcpsalgebra1/ Documents/examviewweb/ev8-4.htm • http://www.regentsprep.org/Regents/math/ALGEBRA/ AV6/indexAV6.htm • http://www.regentsprep.org/Regents/math/ALGEBRA/ AV6/PracFact2.htm