Download 5.4 Factor and Solve Polynomial Equations

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