1 / 7

Synthetic Division

Synthetic Division. Find the remainder of f(x) when divided by x-a. Ex Find the remainder of x 4 +2x 3 - 6x 2 +7x-13 when divided by x-2. Method 1 Using long division. Method 2 Using Synthetic Division. How synthetic division works:. | 1 2 -6 7 -13. 2x1. add. 2. 8. 4. 22.

connor
Télécharger la présentation

Synthetic 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. Synthetic Division Find the remainder of f(x) when divided by x-a. Ex Find the remainder of x4 +2x3 - 6x2+7x-13 when divided by x-2. Method 1 Using long division Method 2 Using Synthetic Division

  2. How synthetic division works: • | 1 2 -6 7 -13 2x1 add 2 8 4 22 _________________________________ 1 4 2 11 9 The quotient is x3+4x2+2x+11. The remainder is 9.

  3. Exercise • Find the remainder when 4x3 +2x-5 • is divided by • x – 3 • x + 5 Finish both parts before you go to the next slide.

  4. Solution Remember that coefficient of x2 = 0. (a) 3 | 4 0 2 -5 12 36 114 _____________________________ 4 12 38 109 Remainder = 28 Write x+5 as x-(-5) (b) -5| 4 0 2 -5 -510 -20 100 ____________________________ -515 4 -20 102 Remainder = -515

  5. Variation From previous example, 4x3+2x-5 when divided by x-3 leaves a quotient 4x2+12x+38 and the remainder is 109. Exercise Find the quotient and the remainder when 4x3+2x-5 is divided by 2x-6.

  6. Solution Since 4x3+2x-5 when divided by x-3 leaves a quotient 4x2+12x+38 and a remainder 109, we can write 4x3+2x-5=(x-3)(4x2+12x+38)+109. To find the quotient and the remainder when 4x3+2x-5 is divided by 2x-6. 4x3+2x-5=(x - 3)(4x2 + 12x+38)+109 =(2x-6)(2x2 + 6x+19)+109 Thus, the quotient is 2x2+6x+19 and the remainder is 109.

  7. Last exercise Find the quotient and remainder when f(x)=4x3+2x2-3x+1 is divided by 2x-1. • Hint: • Write 2x-1 = 2(x-1/2) • Apply synthetic division using x-1/2 • Deduce the quotient and remainder when • f(x) is divided by 2x-1. We shall check the answer in class.

More Related