Polynomials division algebra problem

Question

Find sum of coefficients of the quotient obtained in:

$$\frac{2x^n+x^{n-1}+x^{n-2}+...+x^2+x+5}{x-\frac{1}{2}}$$

I got "n" as the answer but according to the book is wrong, I don't know what is wrong exactly, but i want to know why the answer is "2n" ._. , thanks.

You can always check for $n=3$ if you have doubt. – evil999man Apr 13 '14 at 07:57 — evil999man, Apr 13 '14 at 07:57

score 2 · Accepted Answer · answered Apr 13 '14 at 06:36

2

Using Synthetic division, and see that the bottom row which represents the quotient has the numbers: $2 2 2 ..... 2 6$. There are $n$ $2's$. So the sum of coefficients is: $n\cdot 2 = 2n$

answered Apr 13 '14 at 06:36

DeepSea

77,651

lol thank you, after the site went down i deleted everything and started again, then realized I was dividing wrong. – Harry Apr 13 '14 at 21:23

score 2 · Answer 2 · answered Apr 13 '14 at 09:14

$$\frac{2x^n+x^{n-1}+x^{n-2}+...+x^2+x+5}{x-\frac{1}{2}}=$$

$$\frac{(x-\frac{1}{2})(2x^{n-1}+2x^{n-2}+\dots+2x^2+2x+2)+6}{x-\frac{1}{2}}=$$

$$2x^{n-1}+2x^{n-2}+\dots+2x^2+2x+2+\frac{6}{x-\frac{1}{2}}$$

So the quotient is: $2x^{n-1}+2x^{n-2}+\dots+2x^2+2x+2$

The remainder is: $6$

And the sum of coefficients in the quotient is: $\sum\limits_{i=0}^{n-1}2=2n$

Polynomials division algebra problem

2 Answers2