1 / 8

3.2 The Remainder Theorem

3.2 The Remainder Theorem. Homework from last day. P. 124 #1 – 5 And from Tuesday, p. P. 114 #1, 2, 3, 5, 6, 9, C4. The Remainder Theorem. Given P ( x ) = x 3 - 4 x 2 + 5 x + 1 , determine the remainder when P ( x ) is divided by x - 1. -1. 1 -4 5 1.

nen
Télécharger la présentation

3.2 The Remainder Theorem

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. 3.2 The Remainder Theorem

  2. Homework from last day • P. 124 #1 – 5 • And from Tuesday, p. P. 114 #1, 2, 3, 5, 6, 9, C4

  3. The Remainder Theorem Given P(x) = x3 - 4x2 + 5x + 1, determine the remainder when P(x) is divided by x - 1. -1 1 -4 5 1 The remainder is 3. -1 -2 3 1 -3 2 3 NOTE: P(1) gives the same answer as the remainder using synthetic division. Using f(x) = x3 - 4x2 + 5x + 1, determine P(1): P(1) = (1)3 - 4(1)2 + 5(1) + 1 = 1 - 4 + 5 + 1 = 3 Therefore P(1) is equal to the remainder. In other words, when the polynomial x3 - 4x2 + 5x + 1 is divided by x - 1, the remainder is P (1).

  4. Remainder Theorem: When a polynomial P(x) is divided by x - a, the remainder is P(a).[think x - a, then x = a] Determine the remainder when x3 - 4x2 + 5x - 1 is divided by: a)x - 2 b)x + 1 Calculate P(-1) P(-1) = (-1)3 - 4(-1)2 + 5(-1) - 1 = -1 - 4 - 5 - 1 = -11 Calculate P(2) P(2) = (2)3 - 4(2)2 + 5(2) - 1 = 8 - 16 + 10 - 1 = 1 The remainder is -11. The remainder is 1. Point (-1, -11) is on the graph of of f(x)= x3- 4x2 + 5x - 1 Point (2, 1) is on the graph of of f(x)= x3- 4x2 + 5x - 1

  5. Applications When is divided by the remainder is 30. Determine the value of k.

  6. Problem Solving When the polynomial 3x3 + ax2 + bx -9 is divided by x - 2 , the remainder is -5. When the polynomial is divided by x + 1, the remainder is -16. What are the values of a and b?

  7. Assignment Page 124 6a,7b, 8a,c, 9, 11, 14

  8. Using Synthetic Division 1. (4x3 - 11x2 + 8x + 6) ÷ (x - 2) -2 4 -11 8 6 P(x) = (x - 2)(4x2 - 3x + 2) + 10 -4 6 - 8 4 -3 2 10 2. (2x3 - 2x2 + 3x + 3) ÷ (x - 1) -1 2 -2 3 3 -2 0 -3 P(x) = (x - 1)(2x2 + 3) + 6 2 0 3 6

More Related