Warm-Up 1.) Simplify. (3x-2y3)3 9xy-2 2.) Solve. x6 - 16x4 - 4x2 + 64 = 0 Dec 46:17 PM 5.5 Factor and Remainder Theorems Recall how to long divide: 776 ÷6 Dec 46:11 PM 1 Examples: Divide using polynomial long division. 1.) (3x2 - 11x - 26)÷(x-5) Dec 46:22 PM 2.) (7x3 + 11x2 + 7x + 5) ÷(x2 +1) Dec 46:25 PM 2 3.) (4x4 + 5x - 4)÷(x2 - 3x - 2) Dec 46:26 PM Synthetic Division: Alternative to long division. -Can only be used when dividing by a factor of the form x - k. Examples Divide using synthetic division. 1.) (4x2 - 13x - 5) ÷(x-2) Dec 46:27 PM 3 2.) (x2 + 9)÷(x-3) Dec 46:28 PM 3.) (x3 - 4x + 6)÷(x+3) Dec 46:29 PM 4 ICE: Divide using long division AND synthetic division. (Note: You should get the same answer for each process.) (x4 + 4x3 + 16x - 35)÷(x+5) Dec 46:29 PM Warm-Up 1.) Simplify: (x4 + 5x3 - 4x + 9) - (6x4 -10x2 + 5x3 - 4) 2.) Factor. 125y3 - 64 (Hint: Difference of Cubes) Dec 46:32 PM 5 Examples: Given polynomial f(x) and a factor of f(x), factor f(x) completely. 1.) f(x) = x3 + 6x2 + 5x - 12; x + 4 Dec 46:40 PM 2.) f(x) = 3x3 - 2x2 -61x - 20 ; x - 5 Dec 46:41 PM 6 Examples: Given polynomial function f and a zero of f, find the other zeros. 1.) f(x) = 4x3 - 25x2 -154x + 40 ; 10 Dec 46:49 PM 2.) f(x) = 3x3 + 34x2 + 72x - 64 ; -4 Dec 46:50 PM 7 3.) f(x) = 5x3 - x2 -18x + 8 ; -2 Dec 46:51 PM Dec 69:38 AM 8
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