Adding and subtracting polynomials Multiplying and factoring n

Adding and subtracting polynomials. Multiplying and factoring. n r a e ll l ’ u o y t a Wh To classify, add, and subtract polynomials. To multiply a monomial by a polynomial. To factor a monomial from a polynomial. y r a l u b a c o V Monomial, degree of a monomial, polynomial, Standard form of a polynomial, binomial, trinomial.

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.

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

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

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

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

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

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

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

Problem 1: Finding the degree of a monomial. What is the degree of each monomial? Degree Answers a)1 b)3+2=5 c)0 d)2 e)5 f)0 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

A D A L O V E L A C E

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

When expressions contain like terms, simplify by combining the like terms. Simplify Answer:

Simplify Answer:

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:

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 2 x Factor the expression

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

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