1 / 19

Multiply polynomials.

Objectives. Multiply polynomials. Use binomial expansion to expand binomial expressions that are raised to positive integer powers. Example 1: Multiplying a Monomial and a Polynomial. Find each product. A. 4 y 2 ( y 2 + 3). B. fg ( f 4 + 2 f 3 g – 3 f 2 g 2 + fg 3 ).

kpando
Télécharger la présentation

Multiply polynomials.

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. Objectives Multiply polynomials. Use binomial expansion to expand binomial expressions that are raised to positive integer powers.

  2. Example 1: Multiplying a Monomial and a Polynomial Find each product. A. 4y2(y2+ 3) B. fg(f4 + 2f3g – 3f2g2 + fg3)

  3. Check It Out! Example 1 Find each product. a. 3cd2(4c2d– 6cd + 14cd2) b. x2y(6y3 + y2 – 28y + 30)

  4. To multiply any two polynomials, use the Distributive Property and multiply each term in the second polynomial by each term in the first. Keep in mind that if one polynomial has m terms and the other has n terms, then the product has mn terms before it is simplified.

  5. Example 2A: Multiplying Polynomials Find the product. (a – 3)(2 – 5a + a2)

  6. Example 2A: Multiplying Polynomials Find the product. (a – 3)(2 – 5a + a2)

  7. Example 2B: Multiplying Polynomials Find the product. (y2 – 7y + 5)(y2 – y – 3)

  8. Check It Out! Example 2a Find the product. (3b – 2c)(3b2 – bc – 2c2)

  9. Check It Out! Example 2b Find the product. (x2 – 4x + 1)(x2 + 5x – 2)

  10. Example 3: Business Application A standard Burly Box is p ft by 3p ft by 4p ft. A large Burly Box has 1.5 ft added to each dimension. Write a polynomial V(p) in standard form that can be used to find the volume of a large Burly Box.

  11. Check It Out! Example 3 Mr. Silva manages a manufacturing plant. From 1990 through 2005 the number of units produced (in thousands) can be modeled by N(x) = 0.02x2 + 0.2x + 3. The average cost per unit (in dollars) can be modeled by C(x) = –0.004x2 – 0.1x + 3. Write a polynomial T(x) that can be used to model the total costs.

  12. Example 4: Expanding a Power of a Binomial Find the product. (a + 2b)3

  13. Check It Out! Example 4a Find the product. (x + 4)4

  14. Check It Out! Example 4b Find the product. (2x – 1)3

  15. Example 5: Using Pascal’s Triangle to Expand Binomial Expressions Expand each expression. A. (k –5)3

  16. Example 5: Using Pascal’s Triangle to Expand Binomial Expressions Expand each expression. B. (6m – 8)3

  17. Check It Out! Example 5 Expand each expression. a. (x +2)3 b. (x –4)5

  18. Check It Out! Example 5 Expand the expression. c. (3x +1)4

  19. Lesson Quiz Find each product. 1. 5jk(k – 2j) 2. (2a3– a + 3)(a2+ 3a – 5) 3. The number of items is modeled by 0.3x2 + 0.1x + 2, and the cost per item is modeled by g(x) = –0.1x2 – 0.3x + 5. Write a polynomial c(x) that can be used to model the total cost. 4. Find the product. (y – 5)4 5. Expand the expression. (3a – b)3

More Related