help with dividing polynomials?

Question

how do you do these two problems?

http://img161.imageshack.us/img161/9243/loln00bux5.png

please give an explanation, not just the answer. but an answer would be good too!

Answer 1

It's just like long division. I'll do the first problem for you...

Dividing 4q-7 into 12q^2+7q-1;

4q goes into 12q^2 3q times. So, multiply 4q-7 by 3q:

12q^2-21q

Now, subtract from 12q^2+7q-1 to find the remainder:

(12q^2+7q-1) - (12q^2-21q) = 28q-1

Dividing 4q-7 into 28q-1:

28q/4q = 7, so multiply 4q-7 by 7:

28q - 49

Subtract from 28q-1 to find the remainder:

(28q-1) - (28q - 49) = -1 + 49 = 48

So, the quotient is 3q+7 with a remainder of 48.

To check, multiply 4q-7 by 3q+7:

12q^2+28q-21q-49 = 12q^2+7q-49

Then add the remainder of 48:

(12q^2+7q-49) + 48 = 12q^2+7q-1, which checks.

Answer 2

Treat it like a regular division problem. You want to tackle the higher order terms first and zero them out, then bring the rest down.

For the first, Look at 4q-7 going into 12q^2 + 7q. What do you need to multipe the 4q by to get 12q^2. Once you know, you do the multiplication of that value by the entire polynomial: 4q-7, and subtract it from 12q^2 + 7q - 1. 12q^2 should be eliminated and then you bring down what remains of 7q and the -1, and then repeat.

For the second, this is simliar. Look at what you need to multiply 3y by to get 9y^4. For this one, note that you don't have a value of y^3 in the numerator, so you should imagine a 0y^3 placeholder there.

I'd rather not give an answer if this is homework.

Answer 3

Dividing polynomials is really not that much different from dividing regular expressions. Simply set up the division the same way; try to choose the dividend so that when you multiply by the divisor, you can cancel the first term.

It's kind of difficult to display this here, but here are the answers to your two problems.

1) 3q+7 with a remainder of 50/(4q-7)

2) 3y^3-2y^2+4y+5 with a remainder of 1/(3y+2).

Hope this helps you.

Answer 4

i think the first answer is sthg lik 3q+7 and the second 3y^3-2y^2+4y+5
but i didnt get to finish the problems. soo yeah. the ppl who answered b4 me explained it well... soo good luckk