CP Algebra I
Homework: ________________________________________
8.1 Adding and Subtracting Polynomials
Objectives:
To classify, add, and subtract polynomials
A monomial is ______________________________________________________________________________________________
_______________________________________________________________________________________________________________
Examples:
You can use monomials to form larger expressions called polynomials. Polynomials can be
added or subtracted.
Degree of a monomial: ____________________________________________________________________________________
Finding the Degree of a Monomial: What is the degree of each monomial?
Example 1) 5𝑥
Example 2) 6𝑥 3 𝑦 2
Example 3) 4
Quick Check: What is the degree of each monomial?
1) 8𝑥𝑦
2) −7𝑦 4 𝑧
3) 11
Adding and Subtracting Monomials: You can add or subtract monomials by adding or
subtracting like terms. What is the sum or difference?
Example 4) 3𝑥 2 + 5𝑥 2
Example 5) 4𝑥 3 𝑦 − 𝑥 3 𝑦
Quick Check: What is the sum or difference?
4) −6𝑥 4 + 11𝑥 4
5) 2𝑥 2 𝑦 4 − 7𝑥 2 𝑦 4
Naming a Polynomial Based on Degree and Number of Terms:
Polynomial
6
-2x
3x +1
x 2 + 2x - 5
4x 3 - 8x
2x 4 - 7x 3 - 5x +1
Degree
Classified by
Degree
Number of
Terms
Classified by Term
Classifying Polynomials: Write each polynomial in standard form. What is the name of the
polynomial based on its degree and number of terms?
Example 6) 3𝑥 + 4𝑥 2
Example 7) 4𝑥 − 1 + 5𝑥 3 + 7𝑥
Quick Check:
6) 2𝑥 − 3 + 8𝑥 2
7) 6𝑥 − 𝑥 4 + 3𝑥 2 − 7
8) How does writing a polynomial in standard form help you name the polynomial?
Adding & Subtracting Polynomials: You can do this either vertically or horizontally. I will
show you both ways and you can decide which way you would like to use. Classify the
polynomial by the degree and number of terms AFTER you have done the operation. All answers
should be in standard form.
(
) (
)
Example 8) 3x 2 - 2x +1 + x 2 + 4 x - 3
HORIZONTAL (i.e., GROUP LIKE TERMS)
VERTICAL (i.e., LINE UP LIKE TERMS)
Example 9) ( 5x + 4) - (-2x +3)
10)
HORIZONTAL
HORIZONTAL
VERTICAL
VERTICAL
(3x4 + 4x + 7- 5x) + (-5x4 + 2x3 - 4x2 + 3x - 2)
Quick Check: Add or subtract and then classify by the degree and number of terms
9) (6𝑥 4 − 5𝑥 2 + 3𝑥) + (2𝑥 4 − 8𝑥 2 + 11)
11) (3𝑥 2 + 7𝑥 − 6) + (𝑥 3 + 3𝑥 − 𝑥 − 4)
10) (2𝑥 3 + 6𝑥 2 − 2𝑥 2 − 6) − (5𝑥 3 + 2𝑥 − 2)
12) (5𝑥 4 − 2𝑥 + 7) − (−3𝑥 4 +6x2−5)