Algebra
Name:
Date:
Period:
Exponents and Polynomials
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Page 453 #22 – 59 Left
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Page 453 #25 – 62 Right
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Page 459 #5 – 29 Odd
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Page 459 #14 – 42 First Column; Page 466 #3 – 27 First Column
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Page 459 #15 – 43 Second Column; Page 466 #6 – 30 Fourth Column
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Page 459 #16 – 44 Third Column; Page 466 #31 – 47 Left
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Page 459 #17 – 45 Right; Page 466 #33 – 48 Third Column
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Page 473 #16 – 44 Left *******Quiz Tomorrow********
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Page 580 #19 – 55 Left Every Other One
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Page 580 #21 – 52 Right Every Other One
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Page 587 #9 – 45 Left
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Page 587 #10 – 46 Middle
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Page 587 #11 – 47 Right *******Quiz Tomorrow*******
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Page 593 #16 – 40 Every Other Even
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Applications of Area Problems
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Practice Test for Test Tomorrow
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Page 498 #1 – 10; Page 638 #1 – 7
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8.1 Multiplication Properties of Exponents (R,E/2)
Steps and Laws for Exponents
1. Power to Power - Look for an exponent on the outside of parenthesis
- Rule:
i. Multiply the Exponents
2. Multiplying Monomials – Look for two terms being multiplied together
- Rule:
i. Multiply the Coefficients
ii. Re-write the Variables
iii. Add the Exponents
3. Dividing Monomials – Look for a fraction bar
- Rule:
i. Divide the Coefficients
ii. Re-Write the Variables
iii. Subtract the Exponents Down
4. Combining Like Terms – Look for a + or – sign between two terms
- Rule:
i. Combine the Coefficients
ii. Re-write the variable and exponent
Never:
- Leave an answer in simplest form with a negative exponent (negative exponent property).
- Leave an answer in simplest form with a zero as an exponent (zero exponent property
E1)
a. 53●56
b. x2●x3●x4
c. 3●35
d. (-2)(-2)4
P1)
a. 45●43
b. y3●y4●y5
c. 2●26
d. (-5)(-5)3
E2)
a. (35)2
b. (y2)4
c. [(-3)3]2
d. [(a+1)2]5
P2)
a. (52)3
b. (x3)2
c. [(-2)3]4
d. [(a-2)3]2
E3)
a. (6●5)2
b. (4yz)3
c. (-2w)2
d. –(2w)2
P3)
a. (3●4)2
b. (3xy)4
c. (-3y)2
d. –(3y)2
E4)
Simplify (4x2y)3●x5
P4)
Simplify (3x4y)2●y5
8.2 and 8.3 Zero and Negative Exponents, Division Property of Exponents (R,E/4)
Steps and Laws for Exponents
1. Power to Power - Look for an exponent on the outside of parenthesis
- Rule:
i. Multiply the Exponents
2. Multiplying Monomials – Look for two terms being multiplied together
- Rule:
i. Multiply the Coefficients
ii. Re-write the Variables
iii. Add the Exponents
3. Dividing Monomials – Look for a fraction bar
- Rule:
i. Divide the Coefficients
ii. Re-Write the Variables
iii. Subtract the Exponents Down
4. Combining Like Terms – Look for a + or – sign between two terms
- Rule:
i. Combine the Coefficients
ii. Re-write the variable and exponent
Never:
- Leave an answer in simplest form with a negative exponent (negative exponent property).
- Leave an answer in simplest form with a zero as an exponent (zero exponent property
d. ( )
E1)
a. 2-2
b. (-2)0
c. 5-x
P1)
a. 3-4
b. (-5.2)0
E2)
a. 5(2-x)
b. 2x-2y-3
P2)
a. 4(3-k)
b. 5g-3h-4
E3)
a. 3-2●32
b. (2-3)-2
c. 3-4
P3)
a. 4-3●43
b. (5-2)-3
c. 2-3
c. 4-y
e. 0-3
d. ( )
e. 0-1
E4)
a. (5a)-2
b.
P4)
a. (4y)-3
b.
E5)
a.
b.
c.
d.
P5)
a.
b.
c.
d.
E6)
a. ( )
b. (
P6)
a. ( )
b.
E7)
a.
b. ( )
P7)
a.
b. (
)
c. ( )
( )
c. ( )
)
8.4 Scientific Notation (Multiply and Divide w/ Calculator) (I,E/1)
A number is written in ___________________________ if it is of the form c x 10n, where 1
≤ c < 10 and n is an integer.
E1) Rewrite in decimal form.
a. 2.834 x 102
b. 4.9 x 105
c. 7.8 x 10-1
d. 1.23 x 10-6
P1) Rewrite in decimal form.
a. 3.128 x 103
b. 6.4 x 104
c. 3.9 x 10-1
d. 6.12 x 10-5
d. 0.000722
e. 5,600,000,000
d. 0.0000428
e. 602,000,000
E2) Rewrite in scientific notation.
a. 34,690
b. 1.78
c. 0.039
P2) Rewrite in scientific notation.
a. 52,314
b. 3.2
c. 0.0471
E3) Evaluate the expression. Write the result in scientific notation.
a. (1.4 x 104)(7.6 x 103)
b. (1.2 x 10-1)÷(4.8 x 10-4)
c. (4.0 x 10-2)3
P3) Evaluate the expression. Write the result in scientific notation.
a. (2.5 x 104)(5.8 x 102)
b. (1.82 x 10-1)÷(1.4 x 10-3)
c. (1.5 x 10-4)3
E4) Use a calculator to multiply 0.000000748 by 2,400,000,000.
P4) Use a calculator to multiply 0.00000052 by 3,500,000,000.
10.1 Add and Subtract Polynomials (I,E/2)
An expression which is the sum of terms of the form axk where k is a nonnegative integer is a
______________. Polynomials are usually written in ________________ for, which
means that the terms are placed in descending order, from largest degree to smallest degree.
Polynomial in standard form
Degree
2x3 + 5x2 – 4x + 7
Leading coefficient
Constant term
The ________________ of each term of a polynomial is the exponent of the variable. The
___________________________________ is the largest degree of its terms. When a
polynomial is written in standard form, the coefficient of the first term is the
_____________________________.
A polynomial with only one term is called a _________________. A polynomial with two
terms is called a __________________. A polynomial with three terms is called a
_____________________.
E1) Identify the coefficients of -4x2 + x3 + 3
P1) Identify the coefficients of 4 – x + 2x3
E2)
Polynomial
a.
b.
c.
d.
e.
f.
Degree
Classified By
Degree
Classified By
Number Of Terms
Degree
Classified By
Degree
Classified By
Number Of Terms
6
-2x
3x + 1
–x2 + 2x - 5
4x3 – 8x
2x4 –7x3 – 5x + 1
P2)
Polynomial
a.
b.
c.
d.
e.
f.
-5
(1/4)x
-9x + 1
x2 - 6
-x3 + 2x + 1
3x4 +2x3 – x2+5x -8
E3) Find the sum. Write the answer in standard form.
a. (5x3 – x + 2x2 + 7) + (3x2 + 7 – 4x) + (4x2 – 8 – x3)
b. (2x2 + x – 5) + (x + x2 + 6)
P3) Find the sum. Write the answer in standard form.
a. (-8x3 + x - 9x2 + 2) + (8x2 – 2x + 4) + (4x2 – 1 – 3x3)
b. (6x2 - x + 3) + (-2x + x2 - 7)
E4) Find the difference. Write the answer in standard form.
a. (-2x3 + 5x2 – x + 8) – ( -2x3 + 3x – 4)
b. (x2 – 8) – (7x + 4x2)
c. (3x2 – 5x + 3) – (2x2 –x – 4)
P4) Find the difference. Write the answer in standard form.
a. (-6x3 + 5x – 3) – ( 2x3 + 4x2 – 3x + 1)
b. (4x2 – 1) – (3x - 2x2)
c. (12x – 8x2 + 6) – (-8x2 –3x + 4)
10.2 Multiply Polynomials (I,E/3)
E1) Find the product (x + 2)(x – 3)
P1) Find the product (x + 8)(x – 7)
E2) Find the product (3x - 4)(2x + 1)
P2) Find the product (2x +3)(5x + 1)
E3) Find the product (x – 2)(5 + 3x – x2)
P3) Find the product (x – 4)(5x + 9 –2x2)
E4) Find the product (4x2 – 3x – 1)(2x – 5)
P4) Find the product (5x2 – x – 3)(6x – 5)
10.3 Special Products of Polynomials (I,E/1)
Factored Form
(General)
(a + b)(a – b)
(a + b)2
(a – b)2
Special Product Patterns
Product Form
Factored Form
(General)
(Example)
2
2
a –b
(3x – 4 )(3x + 4)
a2 + 2ab + b2
(x + 4)2
2
2
a – 2ab + b
(2x – 6)2
Product Form
(Example)
9x2 - 16
2
x + 8x + 16
4x2 – 24x + 36
E1) Find the product (5t – 2)(5t + 2)
P1) Find the product (3b – 5)(3b + 5)
E2) Find the product
P2) Find the product
a. (3n + 4)2
b. (2x – 7y)2
E3) Use mental math to find the product
a. 17●23
b. 292
a. (7a + 2)2
b. (2p – 5q)2
P3) Use mental math to find the product
a. 19●21
b. 382
Exponent Applications (Including Area) (I,E/1)
E1) Find an expression for the area of the shaded region.
1
x
1
3
x
3
E2) Find an expression for the area of the shaded region.
1
x
1
3
x
3
E3) Keng creates a painting on a rectangular canvas with a width that is four inches longer than
the height, as shown in the diagram below.
h
h+4
a. Write a polynomial expression, in simplified form, that represents the area of the canvas.
b. Keng adds a 3-inch-wide frame around all sides of his canvas. Write a polynomial
expression, in simplified form, that represents the total area of the canvas and the
frame.
c. Keng is unhappy with his 3-inch-wide frame, so he decides to put a frame with a
different width around his canvas. The total area of the canvas and the new frame is
given by the polynomial h2 + 8h + 12, where h represents the height of the canvas.
Determine the width of the new frame. Show all work and explain each step.