Section 8 – 2 Multiplying & Factoring Objectives: To multiply a monomial by a polynomial To factor a monomial from a polynomial

Problem #1 Multiplying a Monomial and a Trinomial A) Multiple Choice: What is a simpler form of − 𝒙 𝟑 (𝟗 𝒙 𝟒 −𝟐 𝒙 𝟑 +𝟕)? −𝟗 𝒙 𝟏𝟐 +𝟐 𝒙 𝟗 −𝟕 𝒙 𝟑 C) −𝟗 𝒙 𝟕 −𝟐 𝒙 𝟑 +𝟕 𝟗 𝒙 𝟕 −𝟐 𝒙 𝟔 +𝟕 𝒙 𝟑 D) −𝟗 𝒙 𝟕 +𝟐 𝒙 𝟔 −𝟕 𝒙 𝟑

Problem #1 Multiplying a Monomial and a Trinomial B) What is a simpler form of 𝟓𝒏(𝟑 𝒏 𝟑 − 𝒏 𝟐 +𝟖)?

Problem #1 Got It? Simplify each expression. 1) 𝒙 𝟐 (𝟑𝒙 𝟑 −𝟐 𝒙 𝟐 +𝟖) 1) 𝒙 𝟐 (𝟑𝒙 𝟑 −𝟐 𝒙 𝟐 +𝟖) 2) 𝟔𝒙(𝟐𝒙 𝟑 +𝟕𝒙)

Greatest Common Factor (GCF) 1) Find the greatest number that divides evenly into the coefficients of each term 2) Determine the least exponent of each variable

Problem #2 Finding the Greatest Common Factor A) What is the GCF of the terms of 𝟓𝒙 𝟑 +𝟐𝟓 𝒙 𝟐 +𝟒𝟓𝒙?

Problem #2 Finding the Greatest Common Factor B) What is the GCF of the terms of −𝟔𝒙 𝟒 −𝟏𝟖 𝒙 𝟑 −𝟏𝟐 𝒙 𝟐 ?

Problem #2 Got It? Find the GCF of the terms of each polynomial? 1) 2)

Problem #3 Factoring Out a Monomial A) What is the factored form of 𝟒 𝒙 𝟓 −𝟐𝟒 𝒙 𝟑 +𝟖𝒙?

Problem #3 Factoring Out a Monomial B) What is the factored form of 𝟗𝒙 𝟔 +𝟏𝟓 𝒙 𝟒 +𝟏𝟐 𝒙 𝟐 ?

Problem #3 Got It? 1) 6 𝒙 𝟑 −𝟏𝟓 𝒙 𝟐 +𝟏𝟐𝒙 2) 𝟔𝒎 𝟐 −𝟏𝟓𝒎 Factor each polynomial. 1) 6 𝒙 𝟑 −𝟏𝟓 𝒙 𝟐 +𝟏𝟐𝒙 2) 𝟔𝒎 𝟐 −𝟏𝟓𝒎

HOMEWORK Textbook Page 495; #10 – 26 Even

To multiply and factor polynomials Section 8 – 2 Continued… Objectives: To multiply and factor polynomials

Problem # 4 Factoring a Polynomial Model A) A helicopter landing pad, or helipad, is sometimes marked with a circle Inside a square so that it is visible From the area. What is the area Of the shaded region of the helipad at the right? Write your Answers in factored form.

Problem # 4 Factoring a Polynomial Model B) A circle with a radius r is cut from a square that has side length 3r. Write an expression in factored form for the shaded area.

Problem # 4 Factoring a Polynomial Model C) A circular mirror is surrounded by a square metal frame. The radius of the mirror is 5x. The side length of the metal frame is 15x. What is the area of the metal frame? Write your answer in factored form.

HOMEWORK Complete 8 – 2 Worksheet