1. Lesson 8-4 Polynomials

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4. Objectives Find the degree of a polynomial Arrange the terms of a polynomial in ascending or descending order

5. Vocabulary Polynomial – a monomial or the sum of monomials Binomial – the sum of two monomials Trinomial – the sum of three monomials Degree of a monomial – the sum of the exponents of all its variables Degree of a polynomial – the greatest degree of any term in the polynomial

6. Polynomials Polynomials can broken down into sums of monomials –Binomial is the sum of two monomialsx 2 - 7 –Trinomial is the sum of three monomialsx 2 + 2x - 7 Degree of the polynomial –Sum of the highest powers of a monomial term 2x – 5x 2 y 3  degree 5 4xy + 7y 3  degree 3 –-37  degree 0 y + 9  degree 1 Order of terms in the polynomial –Ascending: from the lowest degree monomial term to the highest degree monomial term, in degree order -7 + 2x + x 2 –Descending: from the highest degree monomial term to the lowest degree monomial term, in degree order x 2 + 2x - 7

7. Example 1 Monomial, Binomial, or Trinomial Polynomial?Expression a. b. c. d. Yes, has one term. State whether each expression is a polynomial. If it is a polynomial, identify it as a monomial, binomial, or trinomial. monomial none of these trinomial binomial Yes, is the difference of two real numbers. Yes, is the sum and difference of three monomials. No. are not monomials.

8. Example 2 Write a polynomial to represent the area of the green shaded region. WordsThe area of the shaded region is the area of the rectangle minus the area of the triangle. Variablesarea of the shaded region height of rectangle area of rectangle triangle area

9. Example 2 cont Equation AA Answer:The polynomial representing the area of the shaded region is

10. Example 3 c. b. a. Degree of Polynomial Degree of Each Term TermsPolynomial Find the degree of each polynomial. 88 22, 1, 0 30, 1, 2, 3

11. Example 4 A. Arrange the terms of 16 + 14x 3 + 2x – x 2 so that the powers of x are in ascending order. Answer: B. Arrange the terms of 7y 2 + 4x 3 + 2xy 3 – x 2 y 2 so that the powers of x are in ascending order. Answer:

12. Example 5 A. Arrange the terms of 8 + 7x 2 – 12xy 3 – 4x 3 y so that the powers of x are in descending order. Answer: B. Arrange the terms of a 4 + ax 2 – 2a 3 xy 3 – 9x 4 y so that the powers of x are in descending order. Answer:

13. Summary & Homework Summary: –A polynomial is a monomial or a sum of monomials –A binomial is the sum of two monomials, and trinomial is the sum of three monomials –The degree of a monomial is the sum of the exponents of all its variables –The degree of a polynomial is the greatest degree of any term. To find the degree of a polynomial, you must find the degree of each term Homework: –Pg. 434 16-52 even