# Bell Problem Perform the indicated operation. (x -5)(x2 – 5x + 7)

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Bell Problem Perform the indicated operation. (x -5)(x2 – 5x + 7)

5.4 Factor and Solve Polynomial Equations
Standards: Understand patterns Use models to understand relationships

Type Example General Trinomial 2x2 – 3x - 20 Perfect square trinomial x2 + 8x + 16 Difference of two squares 9x2 - 1 Common monomial factor 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 Not Factored Completely 3x(x2 – 4) Factored Completely 2(x +1)(x – 4) 5x2(x2 – 3)

Ex. Factor the polynomial completely.
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. 8x Ex. 64x3 - 1

Factor by Grouping Ex. Factor the polynomial x3 – 3x2 – 16x + 48 completely.

Ex. Factor completely. 16x4 – 81 2p8 + 10p5 + 12p2 x3 + 7x2 – 9x - 63

Ex. What are the real-number solutions of the equation
Ex. What are the real-number solutions of the equation 3x5 + 15x = 18x3?

Ex. Find the real-number solutions of the equation.
4x5 – 40x3 + 36x = 0 2x5 + 24x = 14x3

Homework 5.4 Practice B worksheet #2-28 even

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