Pre-Algebra 13-1 Polynomials Pre-Algebra HOMEWORK Page 654 #1-14

Our Learning Goal Students will be able to classify, simplify, add and subtract polynomials. Pre-Algebra 13-1 Polynomials

Students will be able to classify, simplify, add and subtract polynomials by completing the following assignments. Learn to classify polynomials by degree and by the number of terms. Learn to simplify polynomials. Learn to add polynomials. Learn to subtract polynomials. …..and that’s all folks! Pre-Algebra 13-1 Polynomials

Today’s Learning Goal Assignment Learn to classify polynomials by degree and by the number of terms. Pre-Algebra 13-1 Polynomials

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

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

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 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