1 / 13

5.4 – Apply the Remainder and Factor Theorems

5.4 – Apply the Remainder and Factor Theorems. Divide 247 / 3 8829 / 8 . 5.4 – Apply the Remainder and Factor Theorems. When you divide a polynomial f(x) by a divsor d(x), you get a quotient polynomial q(x) and a remainder polynomial r(x). f(x) / d(x) = q(x) + r(x)/d(x)

burt
Download Presentation

5.4 – Apply the Remainder and Factor Theorems

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. 5.4 – Apply the Remainder and Factor Theorems Divide 247 / 3 8829 / 8

  2. 5.4 – Apply the Remainder and Factor Theorems When you divide a polynomial f(x) by a divsor d(x), you get a quotient polynomial q(x) and a remainder polynomial r(x). f(x) / d(x) = q(x) + r(x)/d(x) The degree of the remainder must be less than the degree of the divisor. One way to divide polynomials is called polynomial long division.

  3. 5.4 – Apply the Remainder and Factor Theorems Example 1: Divide f(x) = 3x4 – 5x3 + 4x – 6 by x2 – 3x + 5

  4. 5.4 – Apply the Remainder and Factor Theorems Example 1b: Divide f(x) = x3 +3x2 – 7 by x2 – x – 2

  5. 5.4 – Apply the Remainder and Factor Theorems Example 2: Divide f(x) = x3 +5x2 – 7x + 2 by x – 2

  6. 5.4 – Apply the Remainder and Factor Theorems Example 2b: Divide f(x) = 3x3 + 17x2 + 21x – 11 by x + 3

  7. 5.4 – Apply the Remainder and Factor Theorems Synthetic division can be used to divide any polynomial by a divisor of the form x – k.

  8. 5.4 – Apply the Remainder and Factor Theorems Example 3: Divide f(x) = 2x3 + x2 – 8x + 5 by x + 3 using synthetic division

  9. 5.4 – Apply the Remainder and Factor Theorems Example 3b: Divide f(x) = 2x3 + 9x2 + 14x + 5 by x – 3 using synthetic division

  10. 5.4 – Apply the Remainder and Factor Theorems

  11. 5.4 – Apply the Remainder and Factor Theorems Example 4: Factor f(x) = 3x3 – 4x2 – 28x – 16 completely given that x + 2 is a factor.

  12. 5.4 – Apply the Remainder and Factor Theorems Example 4b: Factor f(x) = 2x3 – 11x2 + 3x + 36 completely given that x – 3 is a factor.

  13. 5.4 – Apply the Remainder and Factor Theorems Example 5: One zero of f(x) = x3 – 2x2 – 23x + 60 is x = 3. What is another zero of f?

More Related