Date _________
Period_________
Unit 8, Day 1: Adding and Subtracting Polynomials
Objective: To add and subtract polynomials.
A. Vocabulary
Term: A constant, a variable, or the product of a constant and variable(s).
Ex: 2; x; 3y; 4n6; a2b3; 5c7d8
Like Terms: Two or more terms that have the same variables and exponents. The
coefficients do not matter. Ex. -3x and 8x; 5y2 and 6y2; -4a2b3 and 9a2b3
Polynomial: An expression which is the sum or difference of terms.
Monomial: A polynomial with one term.
Ex: 2; x; 3y; 4n6; a2b3; 5c7d8
Binomial: A polynomial with two terms.
Ex: x + 6; 2y – 9; 8a + 7b
Trinomial: A polynomial with three terms.
Ex: x2 + 5x + 6; a2 + 2ab + b2
Degree of a Term: The sum of the exponents of the variables of a term. Ex: the
degree of 5c7d8 is 15.
Standard Form of a Polynomial: A polynomial whose terms are placed in descending
order, from largest degree to smallest degree. Ex: 4x3 - x2 + 5x - 6
Degree of a Polynomial: The largest degree of the terms of a polynomial.
Ex: The degree of 4x3 - x2 + 5x – 6 is 3.
Leading Coefficient: The coefficient of the first term of a polynomial written in
standard form.
Ex: The leading coefficient of 4x3 - x2 + 5x – 6 is 4.
B. Adding and Subtracting Polynomials:
1.) Variables and exponents must be _______________ __________ to add
or subtract like terms.
2.) When adding or subtracting like terms, combine only the
____________________. The ____________________ stay the same.
3.) Distribute negative signs to __________ terms inside parentheses.
4.) Put the terms of polynomial expressions in ______________ __________
(from highest to lowest degree).
C. Examples of Adding Polynomials
1. (6 x − x 2 + 3) + (4 x 2 − x − 2)
Vertical format
Horizontal format
2. ( x 2 − x − 4) + (2 x + 3 x 2 + 1)
Vertical format
Horizontal format
3. Now you try… Find the sum and write the answer in standard form.
a.) (7 + 2 x − 4 x 2 ) + (−3 x + x 2 − 5)
b.) (8 x − 9 + 2 x 2 ) + (1 + x − 6 x 2 )
D. Examples of Subtracting Polynomials:
Remember, subtraction is the same as adding the opposite. For example, 5 – 3
is the same as 5 + (-3). This is important to keep in mind as we learn to add
polynomials.
1. (5 x 2 − 4 x + 1) − (8 − x 2 )
Vertical format
Horizontal format
2. (− x + 2 x 2 ) − (3 x 2 + 7 x − 2)
Vertical format
Horizontal format
3. Now you try… Find the difference and write the answer in standard form.
a.) ( x + 7 x 2 ) − (1 + 3 x − x 2 )
b.) (2 x + 3 − 5 x 2 ) − (2 x 2 − x + 6)
E. Simplify the expression using both methods:
(2 x 2 + 9 x − 4) + (6 x − 3 x 2 + 1) − ( x 2 + x + 1)
Vertical format
Horizontal format
F. Closure:
1. What was our objective in this lesson? ____________________________
_________________________________________________________
2. Rate yourself (circle one)
A. I need more help
B. I think I got it, but could use more practice
C. I am pretty confident and I could probably teach someone else
3. What are the key ideas when adding and subtracting polynomials?
4. Turn to someone sitting next to you and share a vocabulary word and its’
definition that you learned today. Have them repeat that word and its’
definition to you. Make sure you take turns.