1. Holt CA Course 1 12-1Polynomials Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards California StandardsPreview

2. Holt CA Course 1 12-1Polynomials Warm Up Identify the base and exponent of each power. 1. 3 4 2. 2 a 3. x 5 Determine whether each number is a whole number. 4. 0 5. –36. 5 3; 4 2; a x; 5 yes no yes

3. Holt CA Course 1 12-1Polynomials Preview of Algebra 1 Preparation for 10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques. Also covered: 7AF1.2 California Standards

4. Holt CA Course 1 12-1Polynomials Vocabulary polynomial binomial trinomial degree of a polynomial

5. Holt CA Course 1 12-1Polynomials Recall that a monomial is a number, variable, or a product of numbers and variables with exponents that are whole numbers.

6. Holt CA Course 1 12-1Polynomials monomialnot a monomial 3 and 4 are whole numbers. Additional Example 1: Identifying Monomials 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

7. Holt CA Course 1 12-1Polynomials Check It Out! Example 1 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.

8. Holt CA Course 1 12-1Polynomials A polynomial is one monomial or the sum or difference of monomials. A simplified polynomial can be classified by the number of monomials, or terms, that it contains. A monomial has 1 term, a binomial has 2 terms, and a trinomial has 3 terms.

9. Holt CA Course 1 12-1Polynomials Additional Example 2: Classifying Polynomials by the Number of 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 5 + 2.2x 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.

10. Holt CA Course 1 12-1Polynomials Check It Out! Example 2 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.

11. Holt CA Course 1 12-1Polynomials The degree of a term is the sum of the exponents of the variables in the term. The degree of a polynomial is the same as the degree of the term with the greatest degree. A polynomial can be classified by its degree. 4x 2 + 2x 5 + xy + 5 Degree 2 Degree 5 Degree 2 Degree 0 Degree 5

12. Holt CA Course 1 12-1Polynomials Additional Example 3: Classifying Polynomials by Their Degrees Find the degree of each polynomial. A. x + 4 B. 5x – 2x 2 + 6 Degree 1 Degree 0 x + 4The degree of x + 4 is 1. Degree 1 Degree 2 Degree 0 5x – 2x 2 + 6 The degree of 5x – 2x 2 + 6 is 2.

13. Holt CA Course 1 12-1Polynomials Check It Out! Example 3 Find the degree of each polynomial. A. y + 9.9 B. x + 4x 4 + 2y Degree 1 Degree 0 y + 9.9The degree of y + 9.9 is 1. Degree 1 Degree 4 Degree 1 x + 4x 4 + 2y The degree of x + 4x 4 + 2y is 4.

14. Holt CA Course 1 12-1Polynomials Additional Example 4: Physics Application 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 + 40. 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 + 40 –1600 + 2750 + 40 –16(10) 2 + 275(10) + 40 Substitute 10 for t and 275 for v. Simplify. 1190 The rocket is 1190 ft high 10 seconds after launching.

15. Holt CA Course 1 12-1Polynomials Check It Out! Example 4 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 + 20. 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 + 20 –3600 + 3750 + 20 –16(15) 2 + 250(15) + 20 Substitute 15 for t and 250 for v. Simplify. 170 The rocket is 170 ft high 15 seconds after launching.

16. Holt CA Course 1 12-1Polynomials Lesson Quiz noyes trinomialbinomial 5 3 Determine whether each expression is a monomial. 1. 5a 2 z 4 2. 3√x Classify each expression as a monomial, a binomial, a trinomial, or not a polynomial. 3. 2x 2 – 3x – 64. 3m 3 + 4m Find the degree of each polynomial. 5. 3a 2 + a 5 + 266. 2c 3 – c 2