Download Algebra 1B Assignments Chapter 9: Polynomials and Factoring

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Algebra 1B Assignments
Chapter 9: Polynomials and Factoring
9-1
Pages 497-499: #1-5, 11-18, 24-27, 31-41, 72-75
9-2
Pages 501-503: #2-12 even, 13-32, 34-37, 52-64 even
9-3/ 9- 4
Pages 507-510: #5-10, 20, 21, 30-39, 65, 68, 73, 74
Pages 515-516: #2-8 even, 15-17, 26, 27, 32, 33, 42, 44, 47
Quiz
9-1 to 9-3
Worksheet: Review of Polynomials
9-5/ 9-7
Pages 521-523: #6-11, 22-27, 36, 37, 75-77
Pages 531: #1-4, 13-15
9-6/ 9-7
Pages 525-526: #2-12 even, 16-19, 25-27, 31, 44
Pages 531: #8, 10, 11, 25-27, 38
Review
Worksheet: Chapter 9 Review
Test
Chapter 9: Polynomials and Factoring
Page 548: #1-26
Section 9-1
Warm – Up:
Simplify each expression.
1. 2 x  9  7 x  3
2. 6(3 x  4)
3. 7  (2 x  8)  3
4. 5(4 x  1)  2(8 x  6)
Objective: To describe polynomials
To add and subtract polynomials
k
polynomial - An expression which is the sum of terms of the form
nonnegative integer.
ax where k is a
Example #1:
Which of the following is not a polynomial?
2
12
c
5 x y
n
4


a
3
degree of a monomial - The sum of the exponents of its variables.
Example #2:
What is the degree of each monomial?
4 3
7a
2x y
5
6m n
18
standard form - The degrees of the monomial terms decrease from left to right.
leading coefficient - The coefficient of the first term when written in standard form.
degree of a polynomial - The largest exponent of its terms.
Example #3:
Consider the polynomial 7 x  2  5 x
3
 4x
a)
Write the expression in standard form.
b)
What is the leading coefficient?
c)
What is the degree of the polynomial?
2
Classifying Polynomials by Degree:
Degree
Name
0
constant
1
linear
2
quadratic
3
cubic
Classifying Polynomials by Number of Terms:
# of Terms
Name
1
monomial
2
binomial
3
trinomial
Example #4:
Write each expression in standard form. Then name each polynomial by its degree and
number of terms.
3
a)
8x  4x
b)
3w  5  w
c)
2
2
 7
y
d)
6
e)
9  3z
Example #5:
Simplify each sum.
a) (8 a
2
 3 a  9)  (5 a
2
 7 a  4)
2
b) (3  x  6 x )  ( 2 x  x
2
 7)
Example #6:
Simplify each difference.
a) (3c
2
b) ( 6 x
 8 c  1)  (7 c
3
2
 2 c  4)
3
 5 x  3)  (2 x  4 x
2
 3 x  1)
Closure Question:
What is the difference between adding and subtracting polynomials?
Section 9-2
Warm – Up:
Simplify each expression.
1. (4 x
2
 6 x  7)  (2 x
2
 9 x  1)
2. (3 x
2
 5 x  2)  (8 x
2
3. 8(2 y  1)
4. 7(5  2 x )  10(4 x  3)
Find the greatest common factor.
5. 9, 15, 21
6. 12, 20, 28
 x  6)
Objective: To multiply a polynomial by a monomial
To factor a monomial from a polynomial
Example #1:
Simplify each product.
a) 2 g (3 g
2
 7 g  5)
2
b) 3 h ( 4 h
3
 6h
2
 8 h  1)
Example #2:
Simplify. Write in standard form.
a) y ( y  2)  3 y ( y  5)
2
b) a ( a  1)  a ( a
2
 3)
greatest common factor (GCF) - The greatest factor that divides evenly into each term of an
expression.
Factoring a polynomial reverses the multiplication process. To factor a monomial from a
polynomial, find the GCF of its terms.
Example #3:
Find the GCF of the terms.
a) 2 x
4
 10 x
2
 6x
b) 15 c
Example #4:
Factor each polynomial.
a) 16 n
b) 9 z
2
2
c) 14 x
 12 n  24
 15 z
5
 21 x
4
 7x
2
Closure Question:
Explain how to find the GCF of a polynomial.
4
 10 c
3
 25 c
2
Sections 9-3 / 9-4
Warm – Up:
Simplify. Write each answer in standard form.
1. 6 h ( h
2
 8 h  3)
3. w( w  1)  4 w( w  7)
2
2. y (2 y
3
 7)
4. 6 x ( x  2)  x (8 x  3)
Objective: To multiply binomials
Investigate binomial multiplication with “generic rectangles”.
Example #1:
Find each product.
a) ( n  3)(7 n  4)
b) (2 a  5)(6 a  1)
Some pairs of binomials have special products. If you learn to recognize these pairs, finding
the product of two binomials will sometimes be quicker and easier.
Example #2: Difference of Squares Pattern
Find each product.
a) ( x  4)( x  4)
b) (3 a  5 c )(3 a  5 c )
Example #3: Square of Binomial Pattern
Find each product.
a) ( n  7)
2
b) (6 p  2 r )
Example #4:
Find the area of the shaded region. Simplify.
a)
2
b)
Each term of one polynomial must be multiplied by each term of the other polynomial.
Example #5:
Find each product.
a) ( y  4)( 2 y
2
 5 y  9)
b) (5 c
2
 c  3)(6 c  5)
Closure Question:
When multiplying two binomials, how is using the distributive property twice equivalent to
using the FOIL method for multiplying?
Sections 9-5 / 9-7
Warm – Up:
Simplify each product.
1. ( x  2)( x  5)
2. ( a  4)( a  6)
3. ( n  7)( n  7)
4. ( y  3)
Objective: To factor trinomials of the type ax
2
 bx  c
2
(where a = 1)
Look at the warm-up problems to show the idea of factoring.
(You need two numbers whose product is ac and whose sum is b)
Example #1:
Factor x
2
 8 x  15
Example #2:
Factor m
2
 16 m  48
Example #3:
Factor y
2
 6 y  27
Example #4:
Factor d
2
 8d  9
Example #5: Difference of Two Squares
Factor g
2
 25
Example #6: Perfect Square Trinomials
Factor n
2
 20 n  100
Example #7:
Factor x
2
 11 xy  18 y
2
Closure Question:
How can you determine what numbers are used in the binomial factors when factoring
expressions of the type ax
2
 bx  c ?
Sections 9-6 / 9-7
Warm – Up:
Factor out the GCF.
1.
25 x
2
 10 x  15
2. 24 a
3
 32 a
2
 8a
Factor each expression.
3. y
2
 11 y  24
Objective: To factor trinomials of the type ax
4. c
2
2
 6 c  40
 bx  c
(the leading coefficient is not 1)
* Before factoring with two sets of parenthesis, first check to see if a GCF can be factored out.
Example #1:
Factor 3 x
2
 5x  2
Example #2:
Factor 2 k
2
 21k  11
Example #3:
Factor 5 w
2
 6w  8
Example #4:
Factor 6 n
2
 19 n  15
Example #5: Difference of Two Squares
Factor 25 a
2
 64
Example #6: Perfect Square Trinomials
Factor 4 c
2
 36 c  81
Example #7:
Factor 8 y
2
 32 y  14
Example #8:
Factor 18 d
3
 12 d
2
 6d
Closure Question:
What is the first thing you should look for when factoring a trinomial?