Question

Too tired to think. Will give medal to correct answer. This is not a homework question.

Consider two polynomial p(x) and d(x). The degree of p(x) is larger than d(x). Divide p(x) with d(x) and let the quotient be q(x) and remainder be r(x). Find a relationship between degree of p(x), q(x), d(x) and r(x).

Answer 1

Wait. I screwed that up.

Answer 2

okie

Answer 3

Put it in simple wordings, find a relationship between the degree the dividend, the divisor, the quotient and the remainder.

Answer 4

@ganeshie8 The question is fixed.

Answer 5

p(x) = q(x)*d(x) + r(x)

Answer 6

you want to get a relationship between their degrees is it

Answer 7

Yes.... I feel dreadful because of sleep deprivation ahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh.

Answer 8

degree of q = p-d

Answer 9

that much is clear right ?

Answer 10

Yes. Then deg(q)+deg(d)=deg(p)?

I am tirrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrred.

Answer 11

yes that looks good!

Answer 12

And,

deg(r) < deg(d)

Answer 13

THIS IS NOT WORKING AS INTENDED ARGHHHHHHHHHHH! I thought figuring this out could help me distinguish which part of the result of the synthetic division is the quotient and which part of the result is the remainder. How do I figure that out?

Answer 14

are you dividing a polynomial by a linear polunomial like `ax+b` ?

Answer 15

Or a irreducible quadratic over the reals.

Answer 16

Consider below division :

\(\large \dfrac{x^3+2x+1}{x^2+1}\)

x^3+2x+1 = `x` * `(x^2+1)` + `x+1`

Answer 17

ohk...

Answer 18

everything after first "p-d" elements is a remainder

Answer 19

can u copy paste ur last row of synthetic division ?

Answer 20

Wait. Isn't everything after the first (p-d+1) element is the remainder?

Answer 21

It took me seven seconds to calculate 3-1+1, which is slow. I suppose I am just tired?

Answer 22

Ah yes (p-d+1) looks correct because of the constant term !

Answer 23

lol happens haha! you must have tried something like

3-1+1 = 2+1-1+1 = 2+0+1 = 3

?

Answer 24

I do it like this:
3-1+1
=2+1 (2 seconds)
=3 (2 seconds)

Then I have to do it again because I usually make stupid mistakes! That took me around 8 seconds total actually!

Answer 25

If you want a laugh, this is a good article on science and evolution.

http://sciencealert.com.au/features/20141509-26177.html

Answer 26

lol that's a convincing theory :P ty for shairng ;)