# Sharing the Booty

## OBJECTIVE: To learn how to find the product or quotient of monomials and polynomials

Let's begin this lesson by learning some algebraic terminology. Term - a numeral (number), a variable (letter), a product, or a quotient of a numeral and one or more variables. Examples: 5, x, 2x, 3x2, -7x2y3. Like terms - terms that have the same variable factors or that are both numerals. Examples: 3 and 5 are like terms, x and 2x are like terms, 5x2 and -7x2 are like terms, but 5x and 2y are not like terms. Polynomial - algebraic expression consisting of one monomial or the sum or difference of monomial terms. Examples: 7, x2, 2x3 + 3y - 7, a4 - 8ab + 3b3 - 5. Monomial - a polynomial consisting of exactly one term. Examples: 5, x, 7y, -10x2y2, 12a4b5c6. Binomial - a polynomial consisting of a sum or difference of exactly two terms. Examples: 5 - x3, 9xy + 3, -11xy2z + 2abc3. Trinomial - a polynomial consisting of a sum or difference of exactly three terms. Examples: a + b - c, 2x + 3y + 9, -15x2y4 + 3yz - 4xz5. Degree of a monomial - the sum of the exponents of all its variables. Example: The degree of the monomial -4x4y7z8 is 19. Degree of a polynomial - the highest degree of any of its monomial terms. Example: The degree of the polynomial 10x10 - 2x3y4z5 + 45a7b4 + 100 is 12 because the degree of each monomial from left to right are 10, 12, 11, and 0, and the highest is 12. Simple form - when a polynomial has no like terms and all terms appear in decreasing degree with respect to a given variable, the polynomial is said to be in simple form with respect to that variable. Example: The polynomial 2x3y + 7x2 - 2xy + 11 is in simple form with respect to x.

## TRY IT YOURSELF ...

Below is a set of problems that require you to find the product or quotient of monomials and polynomials. First, solve the problems on scratch paper. Then check the Answer Box below for the correct answers. REMEMBER: You can add or subtract exponents only if you have COMMON bases. Watch out for tricky problems!

## Product or Quotient of Monomials and Polynomials

Check out the answers to the above problems here.

## TODAY you learned how to find the product or quotient of monomials and polynomials.

In future lessons, you'll learn how to perform algebraic operations on other polynomials. Hope you ENJOYED the lesson today.