Name: _____________________________
Date: _____________________________
MATHPOWER CHAPTER 4 NOTES – Polynomials
Date:
4.1 & 4.2/4.3 – Polynomials Intro & Adding/Subtracting
_______________
4.5/5.3 – Multiplying Monomials by Monomials
Multiplying a Polynomial by a Monomial
_______________
1.9 – Powers of Monomials
_______________
4.7/5.4 – Dividing Monomials by Monomials
Dividing Polynomials by Monomials
_______________
Review: _______________
Test: _______________
What You’ll Learn:
4.1 – Using correct vocabulary to describe polynomials
4.2/4.3 – Performing addition and subtraction of polynomials using like terms
4.5/5.3 – Performing multiplication on monomials and polynomials using exponent laws
1.9 – Performing operations on polynomials involving exponents
4.7/5.4 – Performing division on monomials and polynomials using exponent laws
What is a term?
What is a polynomial?
4.1 – Polynomials & 4.2/4.3 – Adding & Subtracting Polynomials_____________
Focus: Classifying, ordering, adding & subtracting polynomials.
Warmup:
How many terms does
each expression have,
and what are they?
a) y + 7 b) x2 – 2x + 3
c) -1 d) 2t – 9 + t3 – t2
e) 2x2y5z7
What is a monomial?
What is a binomial?
What is a trinomial?
What is a polynomial?
ex1 – Classify each
expression:
a) x – 2y
b) -17x2y2z2
c) 4x
d) 2x2 – 5 + 16xy
e) x + y – z + 5
What is the ‘degree’ of
a monomial?
ex2 – State the degree
a) 2x
b) -3x2y3z
c) -7
What is the degree of a
polynomial?
ex3 – State the degree
for each polynomial
a) x2 + 3x + 7
b) 3y – 2y3 + 2y2
c) 4x6 + 2x3y4
d) 25x3y + 36x2y2
ex4 – State the degree
for ‘x’ of each polynomial
a) x2 + 3x + 7
b) 3y – 2y3 + 2y2
c) 4x6 + 2x3y4
d) 25x3y + 36x2y2
How do you order a
polynomial?
Ex4 – Arrange in
descending powers
of x
a) 3x – x2 + 2x3 – 6
b) 2x2y5 – 3x + 2x3y2
4.2/4.3 Warmup:
Simplify:
x2 – 2x + 5x – 3x2
What are like terms?
How do you
add/subtract like terms?
ex1 - Add
(2x2 + 3x + 2) +
(x2 + 2x + 3)
What steps are involved
in adding polynomials?
ex2 – Simplify
a) (3y2 – 8y + 3) +
(2y2 + 8y – 9)
b) (5x3 + 7x – 9) +
(-8x + 11 + 4x3)
Subtracting Polynomials
ex3 - Simplify
(4x2 – 5x + 7) –
(3x2 + 2x – 5)
What is the extra step
needed when
subtracting
polynomials?
ex4 - Simplify
a) (3y2 – y + 5) –
(4y2 – y + 1)
b) (-x2y + 3xy) –
(4xy2 + xy – 2x2y)
Reflection: When rearranging terms, what do you have to make sure of? Explain using
the example: 7 – 3x – 2x2
4.5 – Multiplying Monomials by Monomials
5.3 – Multiplying a Polynomial by a Monomial __________________
Focus: How to multiply two monomials so only one monomial results.
How to multiply a monomial to a polynomial.
Warmup:
Simplify in power form:
a) 32 x 35
b) (-7)4(-7)
c) y6 x y3
What is the shortcut
for multiplying powers
with the same base?
ex1 - Multiply
(6x2)(-3x)
What are the steps to
multiplying monomials?
ex2 - Multiply
a) (3a)(4b3)
b) –x2(2xy)
c) -2y3(4y2)
ex3 – Simplify
a) (2x2y)(-3xy)
b) (x3)(-3xy3)(4y)
c) (-2a3bc2)(-5ac4y2)
ex2 – Expand
a) 2x(x – 6)
b) –y(y2 – 7)
c) m(m + 2) - 3m(m – 5)
ex3 - Simplify
a) 4x(x2 – x + 7)
b) y(y + 3) – y(y – 2)
c) 3(x2 + 2x – 5) – x(x + 1)
Reflection: When distributing into brackets, what exponent rule do you often use?
Then, when adding and subtracting in the last step, explain how to collect like terms?
________________________1.9 – Powers of Monomials____________________________
Focus: How to work with monomials that have an exponent.
Warmup:
Simplify in power form:
a) (34)5
b) (92)3
c) (x6)2
What is the shortcut
when you have an
exponent raised to an
exponent?
ex1 - Simplify
a) (x2)3
b) (y)4
ex2 – Simplify
(2x2y3)2
ex3 - Simplify
a) (-x2y)2
b) (-2a2bc3)3
ex4 - Simplify
-(m2n5)0
ex5 - Simplify
a) (2x2y3)4(-xy2)3
b) (ab3c)2(2a2bc2)3
ex6 - Simplify
 2x
 2
 3y



2
Reflection: What is the most difficult part for you and what can you do to improve upon it?
_
4.7/5.4 – Dividing Monomials by Monomials & Polynomials by Monomials_____
Focus: How to divide monomials so only one monomial results, and how to divide a
polynomial to a monomial.
Warmup:
Simplify in power form:
a) 45  43
27
b) 6
2
c) y3  y
What is the shortcut for
dividing powers with
the same base?
ex1 - Divide
8x 2
2x
What are the steps for
dividing monomials?
ex2 - Simplify
a) 16y  4y
b) -12abc  -2bc
c) 18x5y2  -6x2y
ex3 – Divide
21x 5 yz 2
a)
 7 xyz
b)
10m 8 n 5
5m 3 n 2
ex4 – Simplify
2x 2 y
a)
6 x 2 y 4
b)
8a 2 b 4 c 3
a 4 bc 4
ex5 - Divide
5 xyz  10 xy
5 xy
What are the steps
involved?
ex6 - Simplify
18x 2 y 2 z 2  12 x 3 yz 2
a)
6 xyz
b)
 10a 5 b 4  5a 6 b 8
 5ab 4
c)
27 y 3  9 y  18 y 2
9y
Reflection: What do you do if a negative exponent results?
What results when a top term and bottom term perfectly cancel?