1 / 14

Long Division

Long Division. Just like in the 3 rd grade 6x 3 + 19x 2 + 16x – 4 divided by x - 2 x - 2 6x 3 + 19x 2 + 16x - 4. U-Try. (4x 3 -7x 2 – 11x + 5) divided by (4x + 5). Synthetic division. to divide ax 3 + bx 2 + cx +d by (x – k). k. a b c d. ka. k(b-ka).

melba
Download Presentation

Long Division

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. Long Division • Just like in the 3rd grade 6x3 + 19x2 + 16x – 4 divided by x - 2 x - 2 6x3 + 19x2 + 16x - 4

  2. U-Try (4x3 -7x2 – 11x + 5) divided by (4x + 5)

  3. Synthetic division to divide ax3 + bx2 + cx +d by (x – k) k a b c d ka k(b-ka) a b-ka remainder Coefficients of Quotient

  4. Lets try one x4 – 10x2 – 2x + 4 divided by ( x + 3) ( x + 3) k = -3 x4 + 0x3 – 10x2 – 2x + 4 1 0 –10 – 2 4 -3 -3 9 3 -3 1 -3 -1 1 1

  5. x4 + 0x3 – 10x2 – 2x + 4 1 0 –10 – 2 4 -3 -3 9 3 -3 remainder 1 -3 -1 1 1 __ __x3 + __x2 + __x + __ + (x + 3)

  6. You try • 3x3 -17x2 + 15x -25 divided by (x - 5)

  7. Pretty Cool Remainder Theorem Or the PCRT • If a polynomial is divided by (x - k) then the remainder will be f(k)

  8. Let’s try one • Find the remainder of the problem • 9x3 – 16x – 18x2 + 32 divided by (x – 2) f(x) = 9x3 – 16x – 18x2 + 32 f(2) = 9(2)3 – 16(2) – 18(2)2 + 32 f(2) = 9(8) – 16(2) – 18(4) + 32

  9. Is it a root? • If you try synthetic division and there is no remainder, that means k is a solution to f(x) = 0 or … f(k) = 0 A great way to test for roots of higher degree polynomials

  10. The most confusing instructions for any homework problem I’ve ever seen! What they want Take f(x) and divide it by (x - k) Then write (x - k) (quotient) + remainder (x-k) Page 233 problems 39 -46

  11. Divide then divide again to factor 3rd degree polynomials given 2 factors

  12. Lets try a few problems • Page 235 problems • 7 - 15 • 21 - 27 • 51 - 65

More Related