Algebra 1B
Unit 09
Sections Chap 9 sections 1-6
GUIDED NOTES
NAME _________________________
Teacher _______________
Period ___________
Date: ______________________ Section 9‐1: Factors and Greatest Common Factors Prime Number: Composite Number: Prime Factorization: GCF: Example 1: Classify the number as prime or composite. a.) 36 b.) 23 c.) 22 d.) 31 Example 2: Find the prime factorization of 90 Example 3: Find the prime factorization of ‐140 1
Example 4: Factor each monomial a) 12a2b3 b) ‐66pq2 c) 18x3y3 Example 5: Find the GCF a) 15 and 16 b) 36x2y and 54xy2z c) 27a2b and 15ab2c 2
Date: ______________________ Section 9‐2: Factoring by GCF Notes – Part A Example 1: Greatest common factor.
a) 12 and 18
b) 9a2b and 30ab3
Example 2: Factor GCF.
10a3b2 + 15a2b – 5ab3
Example 3: Factor GCF
12a2 + 16a
3
Date: ______________________ Section 9‐2: Solving by Factoring by GCF Notes – Part B Steps:
1. Set equation = 0
2. Factor out GCF
3. Set factors = 0
4. Solve for x
5. Two answers
Example 1
9x2 + x = 0
Example 2
x2 = 7x
Example 3
(d - 5)(3d - 4) = 0
4
Date: ______________________ Section 9‐2: Factoring by Grouping Notes – Part C Example 1: Factor by grouping
x3 + 5x2 – 2x - 10
Example 2: Factor by grouping
21 – 7y + 3x – xy
Example 3: Factor by grouping
4ab + 8b + 3a + 6
Example 4: Factor by grouping
15a – 3ab + 4b - 20
5
Date: ______________________
Section 9-3: Factoring Trinomials x2 + bx + c
Notes – Part A Recall: (x +4)(x – 3)
Example 1: Factor the trinomial.
a) x2 + 6x + 8
b) x2 – 10x + 16
c) x2 + x - 12
Example 2: Factor the trinomial.
a) x2 – 7x - 18
b) x2 + 7x + 12
c) x2 – 12x + 27
6
Date: ______________________
Section 9-3: Solving by Factoring Trinomials x2 + bx + c
Notes – Part B Steps:
1. Set equation = 0
2. Factor the trinomial by product / sum method
3. Set factors = 0
4. Solve for x
5. Two answers
Example 1
x2 + 6x = 7
Example 2
x2 - 7x + 12 = 0
Example 3
n2 – 36 = 5n
7
Date: ______________________
Section 9-4: Factoring Trinomials ax2 + bx + c
Notes – Part A Example 1:
3y2 – 2y – 5
Example 2:
6x2 + 71x – 12
Example 3:
3a3 + 12a2 – 63a
8
Example 4:
3x2 – 42x + 40
Example 5:
6x2 + 23x + 20
Example 6:
6c2 + 13c + 6
9
Date: ______________________
Section 9-4: Solving by Factoring Trinomials ax2 + bx + c
Notes – Part B Steps:
1. Set equation = 0
2. Factor the trinomial by product / sum method
3. Set factors = 0
4. Solve for x
5. Two answers
Example 1:
12x2 + 3x = 2 – 2x
Example 2:
5d2 – 22d + 8 = 0
Example 3:
4a2 – 16a = -15
10
Date: ______________________
Section 9-5: Factoring Difference of Squares
Notes Difference of Two Squares: a2 – b2 = (a + b) (a – b)
Example 1:
a) x2 - 9
b)b2 + 4
c)16x2 – 25y
d)8x2 - 32
11
Solving by Factoring Difference of two Squares
Steps:
6. Set equation = 0
7. Factor the binomial by difference of two squares
8. Set factors = 0
9. Solve for x
10. Two answers
Example 2
a) p 2 – 16 = 0
b) x2 = 25
c) 18x2 – 50 = 0
12
Date: ______________________
Section 9-6: Factoring perfect Squares
Notes Example 1:
b) 9y2 – 12y + 4
b) x2 + 6y + 9
c) 4x2 – 20x + 25
13
Solving by Factoring Perfect Squares
Steps:
11. Set equation = 0
12. Factor the trinomial by product/sum
13. Set factors = 0
14. Solve for x
15. Two answers
Example 2
d) y2 – 4y + 4 = 0
e) x2 + 12x + 36 = 0
f) 4a2 – 12a + 9 = 0
14
Algebra I
Unit 9 Chapter 9
Factoring
Chapter 9 - Factoring
1. ____
9-1 Factors & GCF
a. Skills practice pg. 525
b. Practice pg 526
2. ____
9-2 Factoring using Distributive Property
a. Skills practice pg 531
b. Practice pg 532
3. ____
9-3 Trinomials a=1
a. Skills practice pg 537
b. Practice pg 538
4. ____
9-4 Trinomials
a. Skills practice pg 543
b. Practice pg 544
5. ____
9-5 Difference of Squares
a. Skills practice pg 549
b. Practice pg 550
6. ____
9-6 Perfect Squares
a. Skills practice pg 555
b. Practice pg 556
7. ____
Ch 9 Review