1 / 9

6.7 Multiplying a Polynomial by a Monomial

6.7 Multiplying a Polynomial by a Monomial. CORD Math Mrs. Spitz Fall 2006. Objectives:. After studying this lesson, you should be able to: Multiply a polynomial by a monomial, and Simplify expressions involving polynomials. Assignment. 6.7 Worksheet. Application.

capucine
Download Presentation

6.7 Multiplying a Polynomial by a Monomial

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 6.7 Multiplying a Polynomial by a Monomial CORD Math Mrs. Spitz Fall 2006

  2. Objectives: • After studying this lesson, you should be able to: • Multiply a polynomial by a monomial, and • Simplify expressions involving polynomials

  3. Assignment • 6.7 Worksheet

  4. Application • The world’s largest swimming pool is the Orthlieb Pool in Casablanca, Morocco. It is 30 meters longer than 6 times its width. Express the area of the swimming pool algebraically. • To find the area of the swimming pool, multiply the length by the width. Let w represent the width. Then 6w + 30 represents the length.

  5. This diagram of the swimming pool shows that the area is w(6w + 30) square meters. This diagram of the same swimming pool shows that the area is (6w2 + 30w) square meters. What does this look like? 30 6w + 30 6w A = 30w w A = w(6w + 30) w A = 6w2 • Since the areas are equal, w(6w + 30) = 6w2 + 30w • The application above shows how the distributive property can be used to multiply a polynomial by a monomial.

  6. A. Use the distributive property. 5a(3a2 + 4) = 5a(3a2) + 5a(4) = 15a3 + 20a B. Multiply each term by 5a. 3a2 + 4 (x) 5a 15a3 + 20a Ex. 1: Find 5a(3a2 + 4)You can multiply either horizontally or vertically.

  7. Ex. 2: Find 2m2(5m2 – 7m + 8) Use the distributive property. 2m2(5m2 – 7m + 8) = 2m2(5m2) + 2m2(-7m) + 2m2(8) = 10m4 - 14m3 + 16m2 Ex. 3: Find -3xy(2x2y + 3xy2 – 7y3). Use the distributive property. -3xy (2x2y + 3xy2 – 7y3) = -3xy(2x2y) + (-3xy)(3xy2)+(-3xy)(-7y3). = - 6x3y2 - 9x2y3 + 21xy4

  8. Ex. 4: Find the measure of the area of the shaded region in simplest terms. 5a2 + 3a - 2 = 2a(5a2 + 3a – 2) - 8(3a2 – 7a + 1 = 10a3 + 6a2 – 4a - 24a2 + 56a – 8 = 10a3 - 18a2 + 52a – 8 The measure of the area of the shaded region is 10a3 - 18a2 + 52a – 8. 3a2 - 7a + 1 2a 8

  9. 7 10 Ex. 5: Many equation contain polynomials that must be added, subtracted, or multiplied before the equation is solved. Solve x(x – 3) + 4x – 3 = 8x + 4 + x (3 + x) x(x – 3) + 4x – 3 = 8x + 4 + x (3 + x) x2 – 3x + 4x – 3 = 8x + 4 + 3x + x2 Multiply x2 + x – 3 = x2 + 11x + 4 Combine like terms x – 3 = 11x + 4 Subtract x2 from each side. - 3 = 10x + 4 Subtract x from each side. - 7 = 10x Subtract 4 from each side. - = x Check this result.

More Related