Adding and Subtracting Polynomials Monday, March 3, 2014.
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Transcript of Adding and Subtracting Polynomials Monday, March 3, 2014.
Adding and Subtracting
Polynomials
Monday, March 3, 2014
What are
Mono- is a prefix meaning “one”Bi- is a prefix meaning “two”Tri- is a prefix meaning “three”Poly- is a prefix meaning “many”-nomial is a suffix meaning “terms”Polynomial = Many Terms
Polynomials?
How do we work with
We can perform operations with polynomials (addition, subtraction, multiplication, and division).
When we write polynomials, the standard is to write in descending order of the exponents.
The degree of a polynomial is the highest exponent or sum of the exponents if there are multiple variables.
Polynomials?
Match the polynomial and its degree…
1. 5p2 – 3
2. a3 – 2a2
3. 3 – 6n5 – 8n4
4. -10x4y3 + 6y3 + 4x4y4
A. trinomial degree 8
B. binomial degree 2
C. trinomial degree 5
D. binomial degree 3
Combining Like TermsAdding Polynomials is
really…
Adding the Opposite.Subtracting Polynomials
is really…
Examples:Adding Polynomials
(#1)
(5p2 -3) + (2p2 – 3p3)
Identify like terms and combine them. 5p2 + 2p2 = 7p2
Write in descending order of the exponents.
-3p3 + 7p2 -3
Subtracting Polynomials #(2)
(a3 – 2a2) – (3a2 – 4a3)
Add the opposite, so… (a3 – 2a2) + (-3a2 + 4a3)
Combine like terms… a3 + 4a3 = 5a3 -2a2 + -3a2 = -5a2
5a3 – 5a2
Note: It can be easier if you put
the exponents in order first.
(#16)(-7x5 + 14 – 2x) + (10x4 + 7x + 5x5)
Reorder
-7x5 + 5x5 +10x4 – 2x + 7x + 14
Combine like terms
-2x5 + 10x4 + 5x + 14
Remember, when subtracting,
add the opposite, then reorder.
(#12)(8n – 3n4 + 10n2) – (3n2 + 11n4 – 7)
8n – 3n4 + 10n2 + -3n2 + -11n4 + 7
-3n4 + -11n4 + 10n2 + -3n2 + 8n + 7
Combine like terms
-14n4 + 7n2 + 8n + 7
Practice makes perfect
Classwork –
Adding and Subtracting Polynomials worksheet (1-30)
Practice some more…
Homework –
Adding and Subtracting Polynomials worksheet (1-20)
# 13 and #17-20 are Bonus Problems – Your Exit Ticket is to circle those problems. Please attempt at least one of them.