Download CHAPTER 8 NOTES

CHAPTER 8 NOTES
FACTORING
8.1 Monomials and Factoring- Day 1
1) Factor- Whole numbers that ________________ evenly into a ____________________.
Examples: List the factors:
a) 12
b) 18
c) 36
d) 24
2) Prime Number- A whole number ______________ than 1 whose only factors are ____ and ___________.
Examples:_______________________________________________________________________
3) Composite Number- A whole number ___________________ than 1, that is not __________________.
Examples:________________________________________________________________________
4) Prime Factorization- A whole number ____________________ as a ____________________ of
_____________________ numbers. Factor all the way down to prime numbers.
Examples: Factor Tree
a) 72
b) 140
c) -150
d) 45x³y²
8.1 Monimials and Factoring- Day 2
1) Greatest Common Factor (GCF): The greatest ________________ that is a _________________ of all
the integers. (Variables- If terms contain the same variable- take out the lowest exponent of the variable).
Examples: Find the GCF:
a) 15,
c) 54,
e) 4a7b,
25
63,
b) 24,
180
28ab
36
d) 12a²b,
f) 96y,
90a²b²c
12x,
-8y
8.2 Factor Using Distribute Property- Day 1
1) Factor by taking out the GCF: The ___________________ of the __________________________
property. Take out the greatest number and variable (lowest exponent) that is common to all terms
Example:
Learned- distribute property- a(b + c) = _________ + __________
common factors
a) 8 · 4 + 8 · 5 = __________________
b) 5a + 20 = __________________________
c) 3b + 18 = _____________________
d) 7x - 21y = _________________________
e) 4x³ - 16x² + 8x = ________________________
e) 8x²y + 2xy² - 10xy = _________________
2) Factor by Grouping- use when there are 4 or more terms.
Examples:
a) (4ab + 8b) + (3a + 6)
c) (rs + 5s)(-r - 5)
b) (6x² - 15x)(-8x + 20)
8.2 Factoring Using the Distribute Property- Day 2
1) Solving Equations by Factoring
Examples: Already FactoredSteps- Set each factor equal to zero.
Solve- get variable by itself
a) (d – 5)(3d + 4) = 0
b) (x – 2)(4x – 1) = 0
Examples: Have to FactorSteps- Move terms to the same side- (if needed)
Factor by taking out the GCF
Set each factor equal to zero
Solve- get variable by itself
c)
x² = 7x
d) 7d² - 35d = 0
Name:___________________________________
Chapter 8 Review- Sections 8.1 – 8.2
8.1
1) Factor each monomial completely- (prime factorization)
42x 3 y 2
-100x³yz²
2) Find the GCF:
54a 2 , 18a 3 , 63a 5
32xy, 48yz
8.2
1) Factor each polynomial:
24xy + 36x 2
12ax 3 + 28a 2 x + 32ax
2) Factor by grouping:
8ax + 6x + 12a + 9
5c – 10c 2 + 2d – 4cd
3) Solve the equation by factoring:
(y – 6)(y + 7) = 0
x 2 + 4x = 0
CHAPTER 8 NOTES
8.3 Factoring Trinomials
(Day 1)
To factor a trinomial ( x 2 + bx + c) find 2 integers that:
 Multiply to equal the last term (c)
 And the same 2 integers that add to the middle term (b)
Examples:
1) x 2 + 5x + 6 =
2)
x 2 + 7x + 10 =
3) x 2 - 6x + 8 =
4) n 2 - 8n + 7 =
5) x 2 + 13x + 30 =
6) n 2 - 10n + 21 =
7) x 2 - 4x - 21 =
8) x 2 - x – 6 =
9) n 2 - 7n + 9 =
8.3
Factoring Trinomials (Day 2)
Solving equations by factoring.
 Get all terms to 1 side of the equation so it is equal to zero.
 Factor if needed.
 Set each term = to 0
 Solve- get the variable by itself
 List answers in { }.
Examples:
1) a 2 + 5a – 36 = 0
2) x 2 + 6x – 27 = 0
3) x 2 + 7x = -6
4) x² - 50 = -23x
8.4 Factoring Trinomials with a Coefficient
Review:
Factor the trinomial:
1) y² + y – 20
2) p² - 2p – 35
8.4 Notes
1) 3m² - 8m – 3
2) 6x²+ 5x – 6
3) 18x² - 27x – 5
4) 6x² - 7x + 18
5) 8x² - 4x + 24
6) 4x² + 26x – 48
Steps:
1) Pull out a GCF if possible.
2) List factors of the 1st term.
3) List factors of the 3rd term.
4) Guess and check:
-1st try factors close together (not extremes)
- (x outer terms) + (x inner terms) = middle term
- try factors in different combinations that add to
the middle term.
8.5 Factoring Differences of Squares
Differences of squares- a² - b² = __________ __________
Examples:
1) k² - 25
2) 1 – 49c²
3) b² - 36d²
4) 4h² - 16g²
5) 8x² - 72p²
6) -16 + p²
8.6 Perfect Square Trinomials
Perfect Square Trinomial _______ terms
 ____________ and ____________ numbers / terms are _________________ squares.
 a 2 + 2ab + b 2 = (a + b)(a + b) = (a + b) 2
 a 2 - 2ab + b 2 = (a – b)(a – b) = (a – b) 2
Examples: Is it a perfect square trinomial? If yes, then factor.
1) 4y 2 + 24y + 36
2) 9y 2 - 12y + 4
3) 25x 2 - 30x + 9
4) 49y 2 + 42y + 36
Factor and Solve:
5) a 2 + 12a + 36 = 0