Download Unit 8 chap 8 polynomials notes

Algebra 1B
Unit 08
Sections 8.1-8.2,8.4-8.7
GUIDED NOTES
NAME _________________________
Teacher _______________
Period ___________
1
Date: ______________________
Section 8-1: Multiplying Monomials
Notes – Part A
MULTIPLY MONOMIALS
Monomial:
Constant:
Example #1: Determine if each expression is a monomial. Explain your reasoning.
1.) 17 – s
2.) 8f2g
3.)
¾
4.) xy
5.)
h
k
6.) p + q
7.) x
8.)
abc 8
5
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Product of Powers:
Example #2: Simplify each expression. Show all work!
1.) (r4) (- 12r7)
2.) (6cd) (5c5d2)
3.) (5x7) (x6)
4.) (4ab6) (- 7 a2b3)
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Date: ______________________
Section 8-1: Multiplying Monomials
Notes – Part B
POWERS OF MONOMIALS
Power of a Power:
Example #1: Simplify each expression. Show all work!
1.) { [ (-3)2 ]3 } 2
2.) [ (23)3 ] 2
3.) [ (23)2 ] 3
4.) [ (33)2 ] 4
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Power of a Product:
Example #2: Simplify each expression. Show all work!
1.) (3y5z)2
2.) (5xyz)3
3.) (x2y5)3
4.) 2 (a4b2)7
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Date: ______________________
Section 8-2: Dividing Monomials
Notes – Part A
QUOTIENTS OF MONOMIALS
Quotient of Powers:
Example #1: Simplify each expression. Show all work!
1.)
a 5b 8
ab 3
3.)
78
73
2.)
x 7 y 12
x6 y3
4.)
− 5 pq 7
10 p 6 q 3
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Negative Exponents:
Example #2: Simplify each expression. Show all work!
1.)
3.)
b − 3c 2
d −5
x −6
y −4 z 9
2.)
− 3a − 4 b 7
21a 2 b 7 c − 5
4.)
75 j 3 k − 5
15 j 5 k − 4 l − 8
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Date: ______________________
Section 8-2: Dividing Monomials
Notes – Part B
QUOTIENTS OF EXPONENTS
Zero Exponent:
Example #1: Simplify each expression. Show all work!
 3x 5 y 
1.)  −

 8 xy 7 
0
 12m8 n 7 
3.) 

 8m5 n 10 
2.)
t 3s0
t2
4.)
b 0c8
c2
0
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Power of a Quotient:
Example #2: Simplify each expression. Show all work!
 2 p2 
1.) 

 3 
4
 2c 3 d 
3.) 

 7z 2 
 4c 3 d 2 
2.) 

 5e 4 f 7 
3
 2x5 y 
4.) 

 5xy 7 
3
−3
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Date: ______________________
Section 8-4: Polynomials
Notes
DEGREE OF POLYNOMIAL
Polynomial:
Example #1: State whether each expression is a polynomial. If yes, identify it as a monomial,
binomial, or trinomial.
1.) 6 – 4
2.) x2 + 2xy – 7
14d + 19e 2
5d 4
3.) 26b
4.)
5.) 2x – 3yz
6.) 8n3 + 5n-2
7.) - 8
8.) 4n2 + 5a + a + 9
5
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Degree of a Polynomial:
Example #2: Find the degree of each polynomial.
9.) 12 + 5b + 6bc + 8bc2
10.) 9x2 – 2x – 4
11.) 14g2h5i
12.) 5mn2
13.) -4x2y2 + 3x2 + 5
14.) 3a + 7ab – 2a2b + 16
Example #3: Arrange the terms of each polynomial so that the powers of x are in ascending order.
15.) 16 + 14x3 + 2x – x2
16.) 7y2 + 4x3 + 2xy3 – x2y2
17.) 7x2 + 2x4 – 11
18.) 2xy3 + 5x3 – y2 – 3x2y
Example #4: Arrange the terms of each polynomial so that the powers of x are in descending order.
19.) 6x2 + 5 – 8x – 2x3
20.) 3a3x2 – a4 + 4ax5 + 9a2x
21.) 8 + 7x2 – 12xy3 – 4x3y
22.) a4 + ax2 – 2a3xy3 – 9x4y
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Date: ______________________
Section 8-5: Adding and Subtracting Polynomials
Notes
ADD POLYNOMIALS
Example 1: Find (3x2 – 4x + 8) + (2x – 7x2 – 5). Show all work!
Example 2: Find (7y2 + 2y – 3) + (2 – 4y + 5y2). Show all work!
Example 3: Find
Example 4: Find
3x 2 − 2 x + 1
+ x 2 + 4 x− 3
2x 2 + 5
+ 6− 2 x + 3x 2
. Show all work!
. Show all work!
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SUBTRACT POLYNOMIALS
Example 5: Find (3n2 + 13n3 + 5n) - (7n +4n3). Show all work!
Example 6: Find (6y2 + 8y4 – 5y) - (9y4 – 7y + 2y2). Show all work!
Example 7: Find
Example 8: Find
5x + 4
. Show all work!
− ( − 2 x + 3)
8x+ 4
− (6 x 2 − 3+ x )
. Show all work!
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Date: ______________________
Section 8-6: Multiplying a Polynomial by a Monomial
Notes – Part A
PRODUCT OF MONOMIAL AND POLYNOMIAL
Example 1: Find – 2x2 (3x2 – 7x + 10). Show all work!
Example 2: Find 6y (4y2 – 9y – 7). Show all work!
Example 3: Find -4xy (5x2 – 12xy + 7y2). Show all work!
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Example 4: Simplify 4 (3d2 + 5d) – d (d2 – 7d + 12). Show all work!
Example 5: Simplify 3 (2t2 – 4t – 15) + 6t (5t + 2). Show all work!
Example 6: Simplify 5n (4n3 + 6n2 – 2n + 3) – 4 (n2 + 7n). Show all work!
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Date: ______________________
Section 8-6: Multiplying a Polynomial by a Monomial
Notes – Part B
SOLVE EQUATONS WITH POLYNOMIAL EXPRESSIONS
Example 1: Solve y (y – 12) + y (y + 2) + 25 = 2y (y + 5) – 15. Show all work!
Example 2: Solve b (12 + b) – 7 = 2b + b (-4 + b). Show all work!
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Example 3: Solve -2 (w + 1) + w = 7 – 4w. Show all work!
Example 4: Solve x (x + 2) – 3x = x (x – 4) + 5. Show all work!
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Date: ______________________
Section 8-7: Multiplying Polynomials
Notes – Part A
MULTIPLY BINOMIALS
Example 1: Find
( x + 3)
. Show all work!
× ( x + 2)
Example 2: Find
( y + 8)
. Show all work!
× ( y − 4)
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Example 3: Find
Example 4: Find
( x − 7)
. Show all work!
× ( 6 x + 4)
(9 p− 1)
. Show all work!
× ( 3 p − 2)
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Date: ______________________
Section 8-7: Multiplying Polynomials
Notes – Part B
MULTIPLY BINOMIALS
F – O – I – L:
Example 1: Find (z – 6) ( z – 12). Show all work!
Example 2: Find (x – 5) (x + 7). Show all work!
Example 3: Find (2y + 3) (6y -7). Show all work!
Example 4: Find (5x – 4) (2x + 8). Show all work!
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MULTIPLY POLYNOMIALS
Example #5: Find each product. Show all work! (Hint: Use the Distributive Property)
a.) (4x + 9) (2x2 – 5x + 3)
b.) (y2 – 2y + 5) (6y2 – 3y + 1)
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