Adding and subtracting polynomials. Multiplying and factoring. What you’ll learn To classify, add, and subtract polynomials. To multiply a monomial by a polynomial. To factor a monomial from a polynomial. Vocabulary Monomial, degree of a monomial, polynomial, Standard form of a polynomial, binomial, trinomial.

Monomial: is a number, a variable, or a product Take a note: Monomial: is a number, a variable, or a product of a number and one or more variables. Degree of a monomial: is the sum of the exponents of its variables. Polynomial: is a monomial or the sum of monomials. Degree of a polynomial: in one variable is the same as the degree of the monomial with the greatest exponent.

xy a. c. d. b. Reason no yes yes yes Determine whether each expression is a monomial. Explain your reasoning. xy d. c. b. a. Reason Monomial? Expression The expression involves subtraction, not the product, of two variables. no yes The expression is the product of a number and two variables. is a real number and an example of a constant. yes yes The expression is the product of two variables.

Determine whether each expression is a monomial. Explain your reasoning. b. a. Reason Monomial? Expression yes Single variables are monomials. no The expression involves subtraction, not the product, of two variables. no The expression is the quotient, not the product, of two variables. The expression is the product of a number, , and two variables. yes Example 1-1b

Find the degree of each monomial. Degree of monomial Monomial 3 4 8 3 2 1 Example 4-3a

Find the degree of each polynomial. b. a. Degree of Polynomial Degree of Each Term Terms Polynomial 0, 1, 2, 3 3 2, 1, 0 2 8 8 Example 4-3a

Monomial, Binomial, or Trinomial State whether each expression is a polynomial. If it is a polynomial, identify it as a monomial, binomial, or trinomial. Monomial, Binomial, or Trinomial Polynomial? Expression a. b. c. d. Yes binomial Yes trinomial No none of these Yes monomial Example 4-1a

Monomial, Binomial, or Trinomial State whether each expression is a polynomial. If it is a polynomial, identify it as a monomial, binomial, or trinomial. Monomial, Binomial, or Trinomial Polynomial? Expression a. b. c. d. Yes trinomial No. which is not a monomial. none of these Yes binomial Yes monomial Example 4-1b

Find the degree of each polynomial. b. a. Degree of Polynomial Degree of Each Term Terms Polynomial 2, 1, 3, 0 3 2, 4, 3 4 7, 6 7 Example 4-3b

Problem 1: Finding the degree of a monomial. What is the degree of each monomial? Degree a)1 b)3+2=5 c)0 Degree d)2 e)5 f)0 Answers Problem 2: Adding and Subtracting Monomials Answers Just combine like terms

Take a note: The standard form of a polynomial means that the degrees of its monomials terms decrease from left to right. You can name a polynomial by its degree or by the number of monomials its contains. Your turn: Write each polynomial in standard form. What is the name of the polynomial base on its degree and number of terms. Answers

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Problem 3:Multiplying a Monomial and a Trinomial Use distributive property, applies properties of the exponents and simplify Find Example 6-1a

When expressions contain like terms, simplify by combining the like terms.  Simplify Answer: Example 6-2a

 Simplify Answer: Example 6-2b

Problem 4: Finding the GCF a)What is the GCF of List the prime factor for all terms Identify the factors common to all terms Answer

Problem 5: Factoring Out a Monomial What is the factored form of following polynomials. Answers:

A helicopter landing pad, or helipad Problem 6: A helicopter landing pad, or helipad is sometimes marked with a circle inside a square so that is visible from the air. What is the area of the shaded region of the helipad at the right? Write your answer in factored form. Find the area of the square region x Find the area of the circle To find area of the red area 2x Factor the expression

3x 6x Your turn Suppose the side length of the square is 6x and the radius of the circle is 3x. What is the factored form of the area of the shaded region? 3x 6x Answer:

Classwork odd Homework even TB pgs 477-478 exercises 8-47 TB pgs 483-484 exercises 9-41