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8-4B Solving Quadratic Equations when the Leading
Coefficient isn’t 1.
X-Factor method
If you factor out a GMF: before using the X figure, keep it, after using the X figure, discard it.
Algebra 1 Glencoe McGraw-Hill Linda Stamper
In the previous lesson you factored quadratic trinomials when the leading coefficient wasn’t 1. Today you will use the factors to solve quadratic equations.
05x3x2 2
To solve a quadratic equation set the factors equal to zero and then solve the equations.
01x5x2 01x 05x2
25
x
5x2
1x
Do not confuse instructions. Make sure you understand what it means to:
Factor Solve
15x8x2 15
85 3 3x5x
015x8x2 03x5x
05x 03x 5x 3x
153
85
05x3x23 2
1x 1x
-5- 5 2+ 2
x2
( )( )
Solve.
-10
-3
x2
5x2 2
Do not discard the GMF from step 2.
015x9x6 2 3
Check using FOIL.
Set the factors equal to zero and solve.
0
05x2 01x 03
25
x
5x2
1x
You must keep the greatest
monomial factor that is
pulled out beforebefore using the X figure!
Can you factor out a greatest monomial
factor?
- 3-3
03x4x2 x-
-1
x-
( )( )
3
-4 - 1
Solve by factoring.34xx2
0
03x 01x
3x 1x
( )( )
02x5x3 2
Example 1 Solve.
6
5 + 3
+ 2
x3
3 2
x3
1x3 1x 2x3
Set the factors equal to zero and solve.
02x3 01x 1x
32
x
2x3
0
Can you factor out a greatest monomial
factor?
- 1+ 22
x2
( )( )
011x21x2 2 Example 2 Solve.
-22
21
x2
22
-1
11x2 11x 1x2
01x2 011x 11x
21
x
1x2
- 3+ 6
x2
( )( )
09x3x23 2
Example 3 Solve.
-18
3
x2
6 -3
3x2 3x 3x2
027x9x6 2 3
03x2 03x 03 3x
23
x
3x2
solutiona not
false
0 0
Can you factor out a greatest monomial
factor?
Can you factor out a greatest monomial
factor?
- 6-6- 10
5x22
-10
015x16x4 2 x4x4
( )( )
60
-16
5x2 3x22 3x2
Example 4 Solve.
0
03x25x2 03x2 05x2
25
x
5x2
23
x
3x2
+ 6
6
x2
( )( )
03x7x2 2
6
7 + 1
x2
1
3x2 3x 1x2
Example 5 Solve. 0
01x2 03x 3x
21
x
1x2
Can you factor out a greatest monomial
factor?
Can you factor out a greatest monomial
factor?
1x33 2x33 1x3
+ 3
x9
36
02x9x9 2 x9
+ 6
( )( )
18
9
2x3
Example 6 Solve.
0
01x3 02x3
32
x
2x3
31
x
1x3
- 3+ 4
x4
( )( )
03xx45 2
Example 7 Solve.
-12
1
x4
4 -3
1x4 1x 3x4
015x5x20 2 5
03x4 01x 05 1x
43
x
3x4
solutiona not
false
0
Can you factor out a greatest monomial
factor?
Can you factor out a greatest monomial
factor?
2x92x9 15x5x20 2
0 05x3x2x3 2
1x 1x
-5- 5 2+ 2
x2
( )( )
-10
-3
x2
5x2 2
0x15x9x6 23
x3
Set the factors equal to zero and solve.
05x2 01x 0x3
25
x
5x2
1x
You must keep the greatest
monomial factor that is
pulled out beforebefore using the X figure!
Can you factor out a greatest monomial
factor?
0x33
Example 8 Solve. x15x4x9x2 323
32
x
2x3
+ 4
x6
3x23
49
06x13x6 2 x6
+ 9
( )( )
Example 9 Solve.
36
13
3x2 2x32 2x3
0
02x3 03x2
23
x
3x2
3x22
2-6
03x4x4 2 x4
- 6
x4
( )( )
-12
-4 + 2
3x2 1x22 1x2
Example 10 Solve.
0
01x2 03x2
23
x
3x2
21
x
1x2
Can you factor out a greatest monomial
factor?
Can you factor out a greatest monomial
factor?
x6x26x7x4 22 22 x103x4x14
8-A10 Pages 445-446 # 23–30,54-59.
