Algebra 1 End-of-Course Review
Module Seven: Polynomials
In this module, you will learn about polynomials and how to perform various operations on them.
Introduction to Polynomials
Polynomials are a specific type of mathematical expression that have:
- one or more terms
- variables with only positive whole number exponents
- no variables in the denominators of each term
Polynomials are classified based on the number of terms and the degree.
The standard form of a polynomial is when the polynomial is listed with each term in decreasing order of degree.
Check out some examples of how to classify polynomials based on the degree and the number of terms.
Addition and Subtraction of Polynomials
To add or subtract polynomial expressions, you must combine like terms. Like termsLike terms: 2xy and 3xy; 5x2y and –4x2y; 10x2y2 and –3x2y2 are terms with the same exact “variable part.” Exponents for the variables must be exactly the same.
There are two methods you may use to add/subtract polynomials: the horizontal and vertical methods.
When multiplying or dividing monomials and polynomials, there are "power properties" involving the base and power that may be applied. The division of polynomials is often written as a rational expression.
Take a moment to review the following properties for multiplication and division.
You learned about two different methods to multiply polynomials:
- The Distribution Method - distribute each term of the first polynomial to each term of the second polynomial.
- The Box Method - write the first polynomial down the side of the box with each term in a row of its own and the second polynomial across the top with each term in a column of its own. Multiply each row and column and fill in the result in the corresponding empty box.
Multiply each set of terms in three parts: determine the sign, multiply the coefficients, and multiply the variables. Combine like terms and write the final product in standard form (descending order).
Check out two examples using both methods.
Special ProductsThere are three special products. The first two special products are the result of squaring a binomial. The product is called a Perfect Square Trinomial. And the third special product is called a Difference of Two Squares. Take a look at examples of each special product.
Dividing a Monomial by a Monomial
An expression isn’t technically simplified if it contains negative exponents. Your final answer should always have positive exponents.
Simplify the following expression. Rollover the expression to reveal the quotient.
Dividing a Polynomial by a Monomial
In order to divide a polynomial by a monomial:
- Method 1 - Rewrite the rational expression as separate fractions, placing each term of the numerator over the denominator, and simplify each one.
- Method 2 - Leave the fraction intact and divide each term in the numerator by the denominator.
Be mindful of your signs, especially when the denominator is negative.
Look here for examples of dividing a monomial by a monomial and a polynomial by a monomial using both methods.