Download Solving Polynomial Equations of 3rd Degree and Higher

Solving Polynomial Equations
rd
of 3 Degree and Higher
STEPS:
1. Factor out GCF
2. Factor remaining
quadratic equation
1. If remaining
equation can not
be factored, use
quadratic
formula.
3. Solve all equations
for variable.
#1:
x 3  x 2  12 x  0
x x 2  x  12  0


xx  4x  3  0
x  0 x  4  0 x 3  0
x 3
x  4
Page 8
#3:
x  9 x  18 x  0
x 2 x 2  9 x  18  0
4

3
2

x 2 x  6x  3  0
x2  0 x  6  0 x  3  0
x 3
x0 x6
#7:
x  4x  4x
 4x 2  4x 2
3
2
Page 8
x 3  4 x 2  4 x
 4x  4x
x3  4 x 2  4 x  0


x x2  4x  4  0
xx  2x  2  0
x 0 x2  0 x2  0
x2
x2
#6:
x 4  5x 2  4  0
x2  4 x2 1  0



x  2x  2x 1x 1  0
x2  0
x2
x  2  0 x 1  0 x  1  0
x  2 x  1 x  1
x 3  3x 2  x  0
x x 2  3x  1  0
2
x  0 x  3x  1  0
#1B:

a 1
b  3
c 1
x

Page 8
What do we
do when we
can’t factor?
 b  b 2  4ac
x
2a
  3 
 32  411
21
3 5
x
2
Roots:
 3 5 3 5 
,
0,

2
2 

2 x 5  14 x 4  10 x 3  0
2 x3 x 2  7 x  5  0
2 x3  0 x 2  7 x  5  0
x0
#4B:
a 1
b  7
c5
x


  7  
 7 
21
 415
What do we
do when we
can’t factor?
7  29
x
2
 b  b 2  4ac
x
2a
2
Page 8
Roots:
 7  29 7  29 
,
0,

2
2 

8 x 3  20 x 2  8 x  0
4 x 2 x 2  5x  2  0
4x  0 2 x 2  5 x  2  0
x0
#1M:
a2
b  5
c2
x


  5 
 5
22
What do we
do when we
can’t factor?
5 9 53
x

4
4
 b  b 2  4ac
x
2a
2
Page
10
53 8
x
 2
4
4
53 2 1
x
 
4
4 2
 422
Roots:
1

0,2, 
2

Homework
• Page 8
#2,5,8 TOP
#2 bottom
• Page 10
#2 middle