6.4 D2
February 13, 2016
Unit 5
Unit 5 ‑ Polynomials and Polynomial Functions 6.4 Solving Polynomial Equations
Objective:
You will be able to solve polynomial equations by factoring.
Bell Ringer
Solve the polynomials by graphing. Use the method of
your choice. (The steps for each method are on the
next page.)
1.) x3 - 2x2 = -3
2.) x3 - 19x = -2x2 + 20
1
6.4 D2
Solve by Graphing
There are two ways to solve polynomials by graphing.
Method 1:
Steps:
1.) y =
2.) Enter the right side of the equal sign into y1
3.) Enter the left side of the equal sign into y2
4.) GRAPH
2nd
TRACE
5: intersect
5.) Move the cursor to the left of an intersection point.
6.) Enter three times
7.) Repeat steps 5 and 6 for each intersection point.
Solve by Graphing
There are two ways to solve polynomials by graphing.
Method 2:
Steps:
1.) y =
2.) Enter the right side of the equal sign into y1
3.) Enter the left side of the equal sign into y2
4.) GRAPH
2nd
TRACE
5: intersect
5.) Move the cursor to the left of an intersection point.
6.) Enter three times
7.) Repeat steps 5 and 6 for each intersection point.
2
6.4 D2
Sum & Difference of Cubes
Sum of Cubes:
(a3 + b3) = (a + b)(a2 - ab + b3)
S
O
A
Difference of Cubes:
(a3 + b3) = (a + b)(a2 - ab + b3)
P
List the first five perfect cubes and 103:
13
23
33
43
53
103
Sum & Difference of Cubes
Examples: Factor.
1.) x3 + 8
2.) 8x3 - 1
3
6.4 D2
Sum & Difference of Cubes
You Try
Factor the polynomials.
1.) x3 - 125
2.) 27x3 + 64
3.) 8x3 - 8
4.) x3 + 1000
Sum & Difference of Cubes
Solve 27x3 + 1 = 0.
4
6.4 D2
Sum & Difference of Cubes
You Try
Solve the polynomials.
5.) x3 + 8 = 0
6.) 27x3 - 1 = 0
7.) 27x3 - 64 = 0
5.) x3 - 125 = 0
Homework
Pg. 330
#1, 3, 5, 12 - 20
5