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GUIDED NOTES – Lesson 3-6b Factoring Polynomial Expressions Name: ______________________ Period: ___ Objective: I can factor polynomial expressions applying a variety of methods and/or combinations.Grouping is a factor method most useful when you have ____ terms, starting with ____.1) Factor out GCF (if any).2) Group the first two terms, and the last two terms. Be sure to group the signs as well and add the groups together.3) Factor the GCF out of both groups.4) Remaining binomial should be the same for both groups. Factor the common binomial.EXAMPLES:x3 + 6x2 – 5x – 3012x3 + 2x2 – 30x – 58x3 – 64x2 + x – 8Quad form is helpful when a trinomial isn’t a quadratic, but can be factored like one. We rewrite each polynomial as a trinomial, au2 + bu + c (where u = x2) then factor like a standard trinomial.EXAMPLES:x4 – 9x2 + 14 2x4 – 4x2 – 163x4 – 11x2 + 10-1295400Sum or Difference of Cubesa3 + b3 = (a + b)(a2 – ab + b2)ORa3 – b3 = (a – b)(a2 + ab + b2)400000Sum or Difference of Cubesa3 + b3 = (a + b)(a2 – ab + b2)ORa3 – b3 = (a – b)(a2 + ab + b2)If factoring two terms that are perfect cubes, we can apply the sum or difference of cubes rule to help us factor.1) Make two sets of parenthesis and put the cube root of each term in the first one and keep the sign2) Now work just with the first parenthesis to fill in the second set of parenthesis: a) Square first termb) Multiply two terms and change the signc) Square last term, using a positive signEXAMPLES: Factor using the sum and difference of cubes formulasa) x3 + 8b) x3 + 27c) x3 – 64d) 125x3 – 8 e) 16x3 + 250 ................
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