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Bell Problem Perform the indicated operation. (x -5)(x2 – 5x + 7) 5.4 Factor and Solve Polynomial Equations Standards: 1. Understand patterns 2. Use models to understand relationships Factoring Quadratic Equations Type General Trinomial Perfect square trinomial Difference of two squares Common monomial factor Example 2x2 – 3x - 20 x2 + 8x + 16 9x2 - 1 8x2 + 20x Factor Ex. 5x2 – 17x + 6 Ex. x2 – x – 6 Ex. x2 – 4 Ex. 4x2 + 16x Factoring Polynomials A factorable polynomial with integer coefficients is factored completely if it is written as a product of unfactorable polynomials with integer coefficients Factored Completely 2(x +1)(x – 4) 5x2(x2 – 3) Not Factored Completely 3x(x2 – 4) Ex. Factor the polynomial completely. a. x3 + 2x2 – 15x b. 2y5 – 18y3 c. 4z4 – 16z3 + 16z2 Homework pg. 356 #3-9 all Bell Problem Factor the polynomial completely. x3 – 7x2 + 10x Perfect Cubes Special Factoring Patterns Sum of Two Cubes a3 + b3 = (a + b)(a2 – ab + b2) Difference of Two Cubes a3 - b3 = (a - b)(a2 + ab + b2) Factor Ex. 8x3 + 27 Ex. 64x3 - 1 Factor by Grouping Ex. Factor the polynomial x3 – 3x2 – 16x + 48 completely. Ex. Factor completely. a. 16x4 – 81 a. 2p8 + 10p5 + 12p2 a. x3 + 7x2 – 9x - 63 Ex. What are the real-number solutions of the equation 3x5 + 15x = 18x3? Ex. Find the real-number solutions of the equation. a. 4x5 – 40x3 + 36x = 0 a. 2x5 + 24x = 14x3 Homework 5.4 Practice B worksheet #2-28 even