Download HW Chap 7 Review

Chapter 7 Review
Selected Worked Homework Problems
Factor completely. Show your work.
!
4 x 2 − 8x !
1.
2.
The GCF is 4x
The GCF is 4x
⎛ 4x 2 8x ⎞
4x ⎜
−
!
⎝ 4x 4x ⎟⎠
⎛ 20x 3 10x 2 ⎞
10x 2 ⎜
−
⎝ 10x 2 10x 2 ⎟⎠
= 4x(x − 2)
= 10x 2 ( 2x − 1)
4. 3x 4 + 12x 3 !
!
!
3
20x −10x
The GCF is 3x
⎛ 3x 4 12x 3 ⎞
3x ⎜ 3 +
!
3x 3 ⎟⎠
⎝ 3x
⎛ 9x 2 6x ⎞
3x ⎜
+
⎝ 3x 3x ⎟⎠
= 3x 3 (x + 4)
= 3x(3x + 2)
7.
x 2 + 2x − 24 !
!
!
6. 9x 2 + 6x
The GCF is 3x 3
3
2
9. x 2 + 9x + 14
We need 2 numbers that
multiply to − 24
and SUBTRACT to + 2
!
+6 and − 4 work
We need 2 numbers that
multiply to + 14
and ADD to + 9
+7 and + 2 work
answer: (x + 6) (x − 4)
answer: (x + 7) (x + 2)
Math 100 !
!
!
!
Chapter 7 Review WKD!
©2016 Eitel
16x 2 − 49 !
10.
11.
a 2 − b 2 = (a + b) (a − b)
↓
↓
↓ ↓
↓ ↓
4x 2 + 25 !
The Sum Of 2 Perfect Squares
Does Not Factor or DNF
!
!
16x − 49 = (4x + 7) (4x − 7)
2
13. x 2 + x − 30 !
14. x 2 − 6x + 9
We need 2 numbers that
multiply to − 30
and SUBTRACT to + 1 !
6 and − 1 work
answer: (x + 6) (x − 1)
We need 2 numbers that
multiply to + 9
and ADD to − 6
!
−3 and − 3 work
answer: (x − 3) (x − 3)
5x 2 − 20 !
15.
!
factor out a 5
We need 2 numbers that
multiply to − 48
and SUBTRACT to + 13
−3 and + 16 work
answer: (x − 3) (x + 16)
5(x − 4)
now factor the
!
difference of 2 PS
5(x + 2)(x − 2)
2
2x 2 + 10x + 12 !
18.
20. 4x 2 − 16
the GCF is 4
factor out a 4
factor out a 2
2(x + 5x + 6)
2
now factor the trinominal
4(x 2 − 4)
now factor the
difference of 2 PS
4 (x + 2)(x − 2)
!
2(x + 3)(x + 2)
!
16. x 2 + 13x − 48
!
Math 100 !
!
!
!
Chapter 7 Review WKD!
©2016 Eitel
22. x 4 − 16 !
23. 2x 3 + 18x !
a 2 − b 2 = (a + b) (a − b)
Factor out a 2x
↓
2x(x 2 + 9)
↓
↓ ↓
↓ ↓
x 4 − 16 = (x 2 + 4) (x 2 − 4)
!
(x − 4) can be factored again
the sum of 2 PS
does not factor so
(x − 2) (x + 2) (x 2 + 4)
2x(x 2 + 9)
2
!
25.
!
!
2
6x + x − 2 !
Step 1. The GCF is 1.
6x 2 + 1x − 2 •
Step 2:
6 to get the easy trinomial
x 2 + 1x − 12
Step 3: Factor the easy trinomial ( x + 4 ) ( x – 3 )
4⎞
⎛
Step 4: Divide each constant added or subtracted from x by 6 ⎜ x + ⎟
⎝
6⎠
3⎞
⎛
⎜⎝ x − ⎟⎠
6
2⎞ ⎛
1⎞
⎛
and then reduce each fraction that can be reduced (no mixed numbers) ⎜ x + ⎟ ⎜ x − ⎟
⎝
⎠
⎝
3
2⎠
Step 5: "glide" the denominator of any remaining fractions (if there are any) in front of the x term
Answer:
( 3x + 2 ) ( 2x − 1)
Math 100 !
!
!
!
Chapter 7 Review WKD!
©2016 Eitel
2
27. 8x − 8x + 2
!
!
Step 1. The GCF is 2. Factor out a 2
8x 2 − 8x + 2 = 2 ( 4x 2 − 4x + 1) now factor 4x 2 − 4x + 2
Step 2:
4x 2 − 4x + 1•
4 to get the easy trinomial
Step 3: Factor the easy trinomial x 2 − 4x + 4
x 2 − 4x + 4
(x–2)(x –2)
2⎞
⎛
Step 4: Divide each constant added or subtracted from x by 6 ⎜ x − ⎟
⎝
4⎠
2⎞
⎛
⎜⎝ x − ⎟⎠
4
1⎞ ⎛
1⎞
⎛
and then reduce each fraction that can be reduced (no mixed numbers) ⎜ x − ⎟ ⎜ x − ⎟
⎝
2⎠ ⎝
2⎠
Step 5: "glide" the denominator of any remaining fractions (if there are any) in front of the x term
Do not forget to include the GCF of 2 that was factored out in the first step.
Answer: 2 ( 2x − 1) ( 2x − 1)
Math 100 !
!
!
!
Chapter 7 Review WKD!
©2016 Eitel
Solve for x. Circle your answers:
28. 10x 2 − 6x = 0 !
29.
4x 2 − 9 = 0 !
Factor out 2x
2x(5x − 3) = 0
Set each factor WITH AN X term
equal to zero and solve for x.
Factor the difference of Squares
(2x + 3)(2x − 3) = 0
Set each factor WITH AN X term
equal to zero and solve for x.
!
2x = 0 or 5x − 3 = 0
x = 0 or x =
30.
2x + 3 = 0 or 2x − 3 = 0
3
5
x=
x 2 − 6x + 5 = 0 !
−3
3
or x =
2
2
32. 3x 2 − 3x − 18 = 0
Factor out a 3
Factor the trinominal
3( x 2 − x − 6 ) = 0
(x − 5)(x − 1) = 0
Set each factor WITH AN X term
equal to zero and solve for x.
Factor the trinominal
3 (x − 3)(x + 2)
!
x − 5 = 0 or x − 1 = 0
Set each factor WITH AN X term
equal to zero and solve for x.
x = 5 or x = 1
x − 3 = 0 or x + 2 = 0
x = 3 or x = − 2
Math 100 !
!
!
!
Chapter 7 Review WKD!
©2016 Eitel
33.
x 2 = 18x − 80
Get all the terms on one side
with a zero on the other side.
Make sure the x 2 term is positive.
Move the 18x and − 80 terms by
adding or subtracting them from
both sides of the equation
x2
= 18x − 80
−18x + 80 − 18x + 80
x 2 − 18x + 80 = 0
Now factor the trinominal
(x − 8)(x − 10) = 0
Set each factor WITH AN X term
equal to zero and solve for x.
x − 8 = 0 or x − 10 = 0
x = 8 or x = 10
Math 100 !
!
!
!
Chapter 7 Review WKD!
©2016 Eitel