Determine the remainder if f=3x^4-2x^3+x^2+ax-1 is divided by (x-1)^2.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

We have to find the remainder when f=3x^4-2x^3+x^2+ax-1 is divided by (x-1)^2

(x-1)^2

=> x^2 - 2x + 1

We use long division to divide 3x^4-2x^3+x^2+ax-1 by x^2 - 2x + 1.

x^2 - 2x + 1 | 3x^4-2x^3+x^2+ax-1 | 3x^2 + 4x+6

......................3x^4-6x^3+3x^2

...................-----------------------------

..............................4x^3 - 2x^2 +ax - 1

..............................4x^3 - 8x^2 + 4x

----------------------------------------------

........................................6x^2 +(a-4)x - 1

........................................6x^2 - 12x + 6

-----------------------------------------------

.................................................. +(a + 8)x - 7

Therefore the remainder is (a+8)x -7.

Approved by eNotes Editorial Team

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial