Common Factoring, Simple Trinomials
Recall: Factor fully. a) 4x2 – 8x – 32 b) 3x(x +8) + 5(x+8)Warm up: Find two integers with the given product and sumProduct = 45, sum = 14 Integers: Product = 6, sum = -5 Integers:IntegersProduct SumIntegersProduct SumProduct = -10, sum = 3 Integers: Product = -20, sum = -8 Integers:IntegersProduct SumIntegersProduct SumDefinitions: A hard trinomial is of the form ____________________. Expand (2x + 3)(3x + 4) algebraically and using an area diagram.When we are factoring, we are trying to reverse this process. To factor a hard trinomial ____________________, Always look for the ________________ factor first when factoring a trinomial Find two integers whose product is ________ and whose sum is _______. Then break up the middle term (decompose!)Factor by grouping. Example 1 Factor, if possible.3x2 + 8x + 43x2 + 2x + 4 6x2 – 5x + 1Example 2 Trinomials with Two VariablesFactor 10x2 – 3xy – 4y2Example 3 Remove a Common FactorFactor 16x2 + 26x – 12.Example 4 Simple TrinomialsSimple trinomials are of the form x2+bx+c, so a=1Factor.x2 – 4x – 21x2 – 29x + 28 x2 + 3x – 1895250317500*Do you see a shortcut? Feel free to use this on quizzes and tests!Summary:Always look for a common factor first when factoring a trinomial.To factor ax2 + bx + c, find two integers whose product is ____ and whose sum is __.Then, break up the middle term and factor by grouping.Not all quadratic expressions of the form ax2 + bx + cThe “Swag” Method – an alternate way to factor3x2 + 8x +46x2 – 5x + 110x2 – 3xy – 4y2Homework: pg. 307 #1, 6(pick at least 4 – do as many as it takes to feel comfortable), 2(pick 4 – do you see the trick yet?), 3 (pick 3) ................
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