Classifying Polynomials in Standard Form A necessary skill to prepare for Algebra I

Polynomial “ Poly” means “many” “ Poly” means “many” “nomial” means “term” (mathematically speaking) “nomial” means “term” (mathematically speaking) So, “polynomial” means “many terms” So, “polynomial” means “many terms” ***A polynomial is a collection of many terms in an expression written with sums and differences. (It uses the same variable which may have different exponents in the expression). ***A polynomial is a collection of many terms in an expression written with sums and differences. (It uses the same variable which may have different exponents in the expression).

Standard Form (of a Polynomial) When a polynomial is written in standard form, it’s variables are arranged in order from highest to lowest exponent. When a polynomial is written in standard form, it’s variables are arranged in order from highest to lowest exponent. Sometimes, this may be reversed and written in order from lowest to highest exponent. Sometimes, this may be reversed and written in order from lowest to highest exponent.

Degree of a Polynomial The degree of a polynomial is the degree (power) of the term with the highest exponent. The degree of a polynomial is the degree (power) of the term with the highest exponent.

Terms (in a Polynomial Expression) Terms are the items being added and subtracted. Terms are the items being added and subtracted. Each term can be one of the following Each term can be one of the following Number alone Number alone Variable alone Variable alone Number and variable joined by multiplication Number and variable joined by multiplication

Naming a Polynomial Polynomials have first and last names like people. Polynomials have first and last names like people. The first name comes from the degree (highest power) of the polynomial. The first name comes from the degree (highest power) of the polynomial. The second name comes from the number of terms being added and subtracted in the expression. The second name comes from the number of terms being added and subtracted in the expression.

First Names in Polynomials Constant: When there is no variable present (just a plain real number). Constant: When there is no variable present (just a plain real number). Linear: When the highest degree of your variables is “1” Linear: When the highest degree of your variables is “1” Quadratic: When the highest degree of your variables is “2” Quadratic: When the highest degree of your variables is “2”

First Names continued... Cubic: When the highest degree of your variables is “3”. Cubic: When the highest degree of your variables is “3”. Quartic: When the highest degree of your variables is “4”. Quartic: When the highest degree of your variables is “4”. Nth degree: A description used when degrees higher than 4 exist as your highest degree. Nth degree: A description used when degrees higher than 4 exist as your highest degree.

Last Names in Polynomials Monomial: 1 term Binomial: 2 terms Trinomial: 3 terms Polynomial with ____ terms: description used when there are more than 3 terms.

Sample Named Polynomials Written in Standard Form Make a chart on your paper as directed by the teacher and copy the samples given... (teacher examples in 3-column chart: Expression, Standard Form, Name) Make a chart on your paper as directed by the teacher and copy the samples given... (teacher examples in 3-column chart: Expression, Standard Form, Name)

Create-a-Polynomial Create ONE of each of the following in Standard Form: 1. Cubic Binomial 2. Quartic polynomial with 5 terms 3. Linear Monomial 4. Quadratic Trinomial 5. Sixth Degree Trinomial 6. Constant Monomial 7. Eighth Degree Polynomial with 4 terms

Create-a-Polynomial continued Cubic Monomial 9. Linear Binomial 10. Quadratic Binomial 11. Quartic Trinomial 12. Ninth Degree polynomial with 6 terms