13-1 Polynomials Pre-Algebra Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

Warm Up 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 Pre-Algebra 13-1 Polynomials yes no yes

Problem of the Day If you take a whole number n, raise it to the third power, and then divide the result by n, what is the resulting expression? n2n2 Pre-Algebra 13-1 Polynomials

Learn to classify polynomials by degree and by the number of terms. Pre-Algebra 13-1 Polynomials

Vocabulary monomial polynomial binomial trinomial degree of a polynomial Insert Lesson Title Here Pre-Algebra 13-1 Polynomials

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. Monomials2n, x 3, 4a 4 b 3, 7 Not monomialsp 2.4, 2 x, √x, g2g2 5 Pre-Algebra 13-1 Polynomials

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 Pre-Algebra 13-1 Polynomials A. √2 x 3 y 4

Try This: 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. Pre-Algebra 13-1 Polynomials

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. Pre-Algebra 13-1 Polynomials

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 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. Pre-Algebra 13-1 Polynomials

Try This: 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. Pre-Algebra 13-1 Polynomials

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 Pre-Algebra 13-1 Polynomials

Additional Example 3A & 3B: Classifying Polynomials by Their Degrees 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. Pre-Algebra 13-1 Polynomials

Additional Example 3C: 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. Pre-Algebra 13-1 Polynomials

Try This: Example 3A & 3B 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. Pre-Algebra 13-1 Polynomials

Try This: Example 3C 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. Pre-Algebra 13-1 Polynomials

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 + 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. Pre-Algebra 13-1 Polynomials

Try This: 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 + 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. Pre-Algebra 13-1 Polynomials

Lesson Quiz noyes Insert Lesson Title Here 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 Pre-Algebra 13-1 Polynomials