Identify the base and exponent of each power a 3. x 5 Determine whether each number is a whole number – ; 4 2; a x; 5 yes no yes Warm Up

Polynomials 13.1

Learn to classify polynomials by degree and by the number of terms.

monomial polynomial binomial trinomial degree of a polynomial Vocabulary

The simplest type of polynomial is called a monomial. A monomial is a number or a product of numbers and variables with exponents that are whole numbers. Monomials 2n, x 3, 4a 4 b 3, 7 Not monomials p 2.4, 2 x, √x, g2g2 5

monomialnot a monomial 3 and 4 are whole numbers. Determine whether each expression is a monomial. y does not have a exponent that is a whole number. B. 3x 3 √y A. √2 x 3 y 4 Example: Identifying Monomials

Determine whether each expression is a monomial. A. 2w p 3 y 8 B. 9t 3.2 z monomialnot a monomial 3 and 8 are whole numbers. 3.2 is not a whole number. Try This

A polynomial is one monomial or the sum or difference of monomials. Polynomials can be classified by the number of terms. A monomial has 1 term, a binomial has 2 term, and a trinomial has 3 terms.

Classify each expression as a monomial, a binomial, a trinomial, or not a polynomial. A. xy 2 B. 2x 2 – 4y –2 C. 3x x 2 – 4 D. a 2 + b 2 monomial Polynomial with 1 term. not a polynomial –2 is not a whole number. trinomial Polynomial with 3 terms. binomial Polynomial with 2 terms. Example: Classifying Polynomials by the Number of Terms

Classify each expression as a monomial, a binomial, a trinomial, or not a polynomial. A. 4x 2 + 7z 4 B. 1.3x 2.5 – 4y C. 6.3x 2 D. c 99 + p 3 binomial Polynomial with 2 terms. not a polynomial 2.5 is not a whole number. monomial Polynomial with 1 term. binomial Polynomial with 2 terms. Try This

A polynomial can also be classified by its degree. The degree of a polynomial is the degree of the term with the greatest degree. 4x 2 + 2x 5 + x + 5 Degree 2 Degree 5 Degree 1 Degree 0 Degree 5

Find the degree of each polynomial. A. x + 4 B. 5x – 2x Degree 1 Degree 0 x + 4The degree of x + 4 is 1. Degree 1 Degree 2 Degree 0 5x – 2x The degree of 5x – 2x is 2. Examples: Classifying Polynomials by Their Degrees

Find the degree of the polynomial. C. –3x 4 + 8x 5 – 4x 6 Degree 4 Degree 5 Degree 6 –3x 4 + 8x 5 – 4x 6 The degree of –3x 4 + 8x 5 – 4x 6 is 6. Example: Classifying Polynomials by Their Degrees

Find the degree of each polynomial. A. y B. x + 4x 4 + 2y Degree 1 Degree 0 y + 9.9The degree of y is 1. Degree 1 Degree 4 Degree 1 x + 4x 4 + 2y The degree of x + 4x 4 + 2y is 4. Try This

Find the degree of each polynomial. C. –6x 4 – 9x 8 + x 2 Degree 4 Degree 8 Degree 2 –6x 4 – 9x 8 + x 2 The degree of –6x 4 – 9x 8 + x 2 is 8. Try This

The height in feet after t seconds of a rocket launched straight up into the air from a 40-foot platform at velocity v is given by the polynomial –16t 2 + vt + s. Find the height after 10 seconds of a rocket launched at a velocity of 275 ft/s. Write the polynomial expression for height. –16t + vt + s – –16(10) (10) + 40 Substitute 10 for t, 275 for v, and 40 for s. Simplify The rocket is 1190 ft high 10 seconds after launching. Example: Physics Application

The height in feet after t seconds of a rocket launched straight up into the air from a 20-foot platform at velocity v is given by the polynomial -16t 2 + vt + s. Find the height after 15 seconds of a rocket launched at a velocity of 250 ft/s. Write the polynomial expression for height. –16t 2 + vt + s – –16(15) (15) + 20 Substitute 15 for t, 250 for v, and 20 for s. Simplify. 170 The rocket is 170 ft high 15 seconds after launching. Try This

noyes trinomialbinomial 5 3 Determine whether each expression is a monomial. 1. 5a 2 z √x Classify each expression as a monomial, a binomial, a trinomial, or not a polynomial. 3. 2x – 3x – 64. 3m 3 + 4m Find the degree of each polynomial. 5. 3a 2 + a c 3 – c 2 Lesson Quiz