# Remainder theorem questions

1. Nov 10, 2013

### Ambushes

1. The problem statement, all variables and given/known data
Find each remainder:

a. (x^3 + 5x^2 - 7x + 1) ÷ (x+2)(x-1)

b. (2x^3 + x^2 - 4x - 2) ÷ (x^2 + 4x + 3)

2. Relevant equations

N/A. (We've used Long Division and Synthetic Division for previous questions.)

3. The attempt at a solution

How would i go about solving these? I'm pretty stuck.

2. Nov 10, 2013

### tiny-tim

Hi Ambushes!

Why can't you use long division?​

3. Nov 10, 2013

### Ambushes

I've never done long division with two binomials/zero's before, usually it's only one like (x+2), etc.
What do i have to do differently?

Thanks for the help!

4. Nov 10, 2013

### tiny-tim

nothing!

it's only like the difference between "ordinary" long division by 2 and by 23

5. Nov 10, 2013

### Ambushes

Haha, wasn't as hard as i thought. Got the right answer =).
If you don't mind, i have one more question. It's probably really easy, but how do i know when to use Synthetic Division, and when to use Long Division?

6. Nov 10, 2013

### tiny-tim

hmm … i've never come across synthetic division before

i had a quick look at it on wikipedia, and my impression is that long division would always be easier, and less likely to lead to mistakes

does anyone who's actually used it want to chip in?

7. Nov 10, 2013

### rcgldr

For 1 a, why not multiply the two divisor terms to produce a product of a single polynomial (x^2 + ...) and then continue using long division?

8. Nov 10, 2013

### Dick

Synthetic division is just a streamlined form of the long division algorithm. It does exactly they same thing as long division but omits writing a lot of powers of x. It's not in any way a different thing. There's no need to decide which to use. Use synthetic division if you remember how to do it. Otherwise long division will give you the same answer.

Last edited: Nov 10, 2013
9. Nov 11, 2013

### tiny-tim

thanks, Dick!