Topic Algebraic Expressions 2 Aim How do we

Topic: Algebraic Expressions 2 Aim: How do we multiply/divide a polynomials by a monomial? DO NOW: Simplify. (A) (2 x 3 y)(-3 x 4 y) (B) 45 x 4 y 5 xy (C) (-x 7 y)(-y 2 z)

Review: Multiply Monomials (-2 x 5 y)(4 x 4 yz)

Multiplying a Polynomials by a Monomial Use the DISTRIBUTIVE property to multiply all terms in parenthesis by the term outside the parenthesis. Example: 2 x 2 y(3 xy 4 - 2)

Multiplying Polynomials by Monomials DISTRIBUTIVE PROPERTY!! Multiply using the _____________ #1 2(4 x + 3) #2 -2(x + 4) #3 -2(3 x - 5)

Multiplying Polynomials by Monomials DISTRIBUTIVE PROPERTY!! Multiply using the _____________ #4) 2 x(-8 x + 5 x 2 + y 2) #5) -5 x(2 x 3 + 2 x 2 - 4)

Review: Dividing Monomials 24 x 14 y 15 z 4 6 x 7 y 5 z 4

Dividing Polynomials by Monomials Can we use our knowledge of multiplying polynomials by monomials to help us? Can we use our knowledge of dividing monomials to help us?

Dividing a Polynomial by a Monomial Divide each term in the numerator by the monomial in the denominator. **Remember that terms do not "cancel". They reduce to 1. Example:

Distributive Property Divide Polynomials by Monomials Using the ________________ #6 #7

Distributive Property Divide Polynomials by Monomials Using the ________________ #8 #9

SUMMARY What is the rule when multiplying monomials? What are the rules for dividing monomials? What property must we use to multiply or divide a polynomial by monomial? Do terms ever "cancel'? Explain.

HOMEWORK Complete Handout

Real-Life Applications! #10) Your favorite sport is basketball. You decide you want to know the AREA of the court that you plan on. The length of the court is x inches and width is (3 x + 7) inches. What is the AREA of the basketball court expressed as a polynomial in simplest form? AREA FORMULA: ________

Real-Life Applications! #11) You have fenced off a rectangular play field in your backyard for your new puppy. The length of the play field is x and the width is (x + 5). (a) What is the AREA of the play field expressed in simplest terms? (b) What is the PERIMETER of the play field expressed in simplest terms?

Real-Life Applications! #12) Your town has decided to get a new outdoor swimming pool. The length of the pool is x feet and the width of the pool is (x 2 + 5 x + 4) feet. What is the AREA of the swimming pool as a polynomial in simplest form? AREA FORMULA: ________