1. Polynomial Operations

2. Review of Definitions
A constant is a known number. Ex. -5, ⅓, π, 37, etc.
A variable is a letter that represents an unknown number. Ex. x, y, etc.
A monomial is a constant, variable, or combination of constant and variables. Ex. 5, 5x, 5xyz, 5x2y3z4, x, etc.
If a variable doesn’t have a coefficient or exponent, assume that it’s 1. Ex. x = 1x1

3. Polynomial Addition/Subtraction
When adding or subtracting monomials, the variables and their exponents must match exactly, “like terms”, then add or subtract the constants of the monomial.
Ex. 5x3 + 4x2 = 5x3 + 4x2 since the exponents don’t match.
Ex. 5cx3 + 4x3 = 5cx3 + 4x3 since the variables don’t match.
Ex. 5x3 + x3 = 6x3

4. Assignment
Worksheet on Polynomial Addition and Subtraction

5. Monomial Multiplication
To multiply monomials, multiply the constants and add variable exponents.
Ex. 5x3 ● 4x2 = 20x5
Ex. (3xy3)(7x3y) = 21x4y4

6. Monomial Distribution
To distribute monomials, multiply the monomial outside the parenthesis to any monomials inside the parenthesis.
Ex. 5x (x – 6) = 5x2 – 30x
Ex. (3x + 2) ● (– 4x) = – 12x2 – 8x

7. Assignment
Worksheet on Monomial Distribution

8. Monomial Factoring
With Monomial division you’re given the divisor term (the monomial after the division symbol). Divide all terms inside parenthesis by simplifying coefficients, and subtracting exponents.
Factoring is when you have to find then divide by the Greatest Common Factor, which is the largest factorable constant and variable with the lowest exponent that can be taken from each term in a polynomial.

9. Monomial Factoring Ex. What is the GCF of – 2x2 – 8x?
Ex. What is – 2x2 – 8x factored out?
Ex. Factor: 12x²y – 6xy² – 3xy
Your turn. Factor: 2y – 6xy² – 8xy³

10. Assignment
Worksheet on Monomial Division and Factoring