1 / 4

50 likes | 374 Views

Remainder and Factor Theorems. REMAINDER THEOREM. Let f be a polynomial function. If f ( x ) is divided by x – c , then the remainder is f ( c ). Let’s look at an example to see how this theorem is useful.

Download Presentation
## 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

**REMAINDER THEOREM**Let f be a polynomial function. If f (x) is divided by x – c, then the remainder is f (c). Let’s look at an example to see how this theorem is useful. So the remainder we get in synthetic division is the same as the answer we’d get if we put -2 in the function. The root of x + 2 = 0 is x = -2 using synthetic division let’s divide by x + 2 -2 2 -3 2 -1 -4 14 -32 2 -7 16 -33 the remainder Find f(-2)**FACTOR THEOREM**Let f be a polynomial function. Then x – c is a factor of f (x) if and only if f (c) = 0 -3 -4 5 0 8 12 -51 153 -4 17 -51 161 If and only if means this will be true either way: 1. If f(c) = 0, then x - c is a factor of f(x) 2. If x - c is a factor of f(x) then f(c) = 0. Try synthetic division and see if the remainder is 0 Opposite sign goes here NO it’s not a factor. In fact, f(-3) = 161 We could have computed f(-3) at first to determine this. Not = 0 so not a factor**Acknowledgement**I wish to thank Shawna Haider from Salt Lake Community College, Utah USA for her hard work in creating this PowerPoint. www.slcc.edu Shawna has kindly given permission for this resource to be downloaded from www.mathxtc.com and for it to be modified to suit the Western Australian Mathematics Curriculum. Stephen Corcoran Head of Mathematics St Stephen’s School – Carramar www.ststephens.wa.edu.au

More Related