Review Lesson Monomials

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

Monomial Addition/Subtraction When adding or subtracting monomials, the variables and their exponents must match exactly, 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

Assignment Worksheet on Monomial Addition and Subtraction

Monomial Multiplication and Division To multiply monomials, multiply the constants and add variable exponents. To divide monomials, divide the coefficients, and subtract the variable exponents. Ex. 5x3 ● 4x2 = 20x5 Ex. (3xy3)(7x3y) = 21x4y4 Ex. 8x3 / 4x2 = 2x1

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

Assignment Worksheet on Monomial Multiplication and Distribution

Monomial Factoring With Monomial division you’re given the divisor term (the monomial after the division symbol). Factoring is when you have to find then divide by the Greatest Common Factor, which is the largest constant and variable that can be taken from each term in a polynomial.

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

Assignment Worksheet on Monomial Division and Factoring