Unit 5 ~ Day B ~ Solving Inequalities by Factoring
Solving Inequalities By Factoring –
1.) Set the quadratic inequality, ax2 + bx + c <, >, <, or > 0,
2.) Then factor using the method of your choice.
3.) Since it is easier to use a graphing method to solve these inequalities, graph and then
determine the solution set.
Examples: 1.) x2 - x – 6 < 0
(x – 3)(x + 2) < 0 (one factor must be positive & one factor must be
negative for this to be true)
(Use the number line to see what happens around x= 3 & x= -2)
x-3
------------------------------- ---------------------
+++++++++++++
x+2
------------------------------- ++++++++++++
++++++++++++++
.
-6 -5 -4 -3 -2 -1 0
1
2
3
4
5
6
So the solution set will be the region where one factor is positive & one is negative.
Solution Set = {x -2 < x < 3 }
2.) x3 - 4x2 - 4x + 16 > 0
(x3 - 4x2)+(- 4x + 16) > 0 Factor by Grouping
x2 (x – 4) – 4(x – 4) > 0
(x – 4)(x2 – 4) > 0
(x – 4)(x – 2)(x + 2)>0 For this to be true all factors must be positive or
one factor is positive & two factors are
negative
Use the number line to see what happens around x= 4, x= 2, x= -2
x - 4---------------
--------------
x - 2------------- ---------------x + 2-------------- ++++++++++
-6 -5 -4 -3 -2 -1 0
1
2
-------
++++++
++++
++++
++++++
++++++
3
4
5
6
So the solution set will be the regions where the product of three factors is positive.
Solution Set = {x - 2 < x < 2 or x > 4 }
Remember…
Solve:
1.
x+7>0
2.
2x – 8 < 0
3.
4x + 2 ≤ 0
4.
x2 – x – 6 < 0
5.
2x2 – x – 3 ≥ 0
6.
3x2 – 22x – 16 > 0
7.
12x2 + 2x ≥ 2
8.
x2 – x – 12 < 0
9.
4x2 + 12x + 9 > 0
10.
6x2 – 2x – 25 > -5
11.
25x2 – 16 ≤ 0
12.
8x2 – 15x – 2 ≥ 0
13.
100x2 – 400 > 0
Solve by factoring and test point method:
Graph your solution. Then write it in interval notation.
1. 4x2 – 8x + 3 < 0
2. (x + 1)(x – 3) > 0
3. x2 + 5x + 6 > 0
4. x2 + x – 20 < 0
5. x2 – 4 ≤ 0
6. 4x2 – 9x + 2 < 0
7. 2x2 + 5x – 12 ≥ 0
8. 16x2 – 81 ≥ 0
9. 9x2 – 25 > 0
Unit 5 Day B HW Answer Key:
1 3
1.  , 
2 2
2.
 , 1 or  3,  
3.
 , 3 or  2,  
4.
 5, 4 
3
9
9
5 5 
1 

5.  2, 2 6.  , 2  7. (-,-4] or [ , ) 8. (,  ]or[ , ) 9.  ,   or  ,  
2
4
4
3 3 
4 
