Chapter Seven Polynomials Algebra One

Monomials What is a monomial? A monomial is a number, a variable or a product of a number and one or more variables. Which of the following is a monomial?   

Rules Here are the basic rules 4.

Multiplying Do you notice that the bases are the same? How could we make this easier to understand? RIGHT! Use numbers instead of letters

Check multiplying

Dividing OR

Power of a power

Power of a product

Power of a quotient

Zero Exponent Since anything over itself is equal to 1, then anything to the zero power is equal to 1

Power of one Anything raised to the power of one, is itself

Negative Exponent

Polynomials A polynomial is a monomial or a sum of monomials. What does that mean???? Each “thing” in the expression must be a monomial as defined previously. Then if the monomials can be added, the expression is called a polynomial.

For Example This IS a polynomial, also called a binomial because it has two monomials. This IS a polynomial, also called a trinomial because it has three monomials. This IS NOT a polynomial, because is NOT a monomial

Degrees of Polynomials The degree of a monomial is the sum of the exponents of its variables The degree of a polynomial is the greatest of the degrees of its terms. In other words, to find the degree of the polynomial, add up EACH of the degrees of the monomials and pick the biggest one.

Lets try some! First, why is it important? Find the degree of each of the following polynomials. Now you make one up and tell the person next to you what the degree is.

Adding and Subtracting Polynomials For all operations with polynomials, it is CRUCIAL to remember what LIKE TERMS are. If I had a nickel for every time I said “combine like terms”… so you MUST know what this means. Like terms are terms that contain the same variables, with corresponding variables having the same power.

Practice Simplify the following expression