Question

(x^8+x^6)/(x-1)
Is there an easier way to find the remainder without dividing it out?

Answer 1

1. After you divide you'll get a whole number and a decimal.
2. subtract the whole number part.
3. You'll now have the decimal part only which will be less than one.
4. multiply this by the original number you divided by.
5. The result (you'll need to round it) is the remainder.

Example

99/13 = 7.61538461538461
Subtract 7 to get: 0.61538461538461
multiply the above by 13 to get: 7.99999999999999
rounding gives you the remainder of 8.
This the the remainder when you divide 99 by 13.

hope this helps. is pretty accurate to check your work.

Answer 2

.... I don't get it.

Answer 3

Where are these numbers coming from?

Answer 4

The example ??? or do you want to work out your problem?

Answer 5

Oh. That was an example? I wanted to find the remainder WITHOUT diving to find the quotient.

Answer 6

dividing*

Answer 7

Btw, you could avoid all of that if you use long division.

Answer 8

Just plug in x = 1.

Answer 9

1/0.

Answer 10

Into the top expression.

Answer 11

2.

Answer 12

is that it?

Answer 13

Yes.

Answer 14

Have you considered Synthetic Division?

Answer 15

@tkhunny Why bother? Remainder Theorem.

Answer 16

I have, but when the degrees are too big, it's trouble some. ex.x^64+x^43/(3x-4)

Answer 17

Then, you'll have way too many zeroes.

Answer 18

the remainder is what you get when you replace the \(x\) in the numerator by \(1\)

Answer 19

@Grazes I've told you what to use. It works.

Answer 20

Right. Thanks.

Answer 21

Well, it is very little trouble and it gives both the remainder and the whole quotient. Perhaps I was over doing it.

Indeed, Synthetic Division is not recommended for massive degree unless there is some convenient simplification.