SOLUTION: I'm learning to divide polynomials by polynomials. I have been able to work several problems, but then get stuck as they progress. For example: 25x to the 5th power take away

Question 119164: I'm learning to divide polynomials by polynomials. I have been able to work several problems, but then get stuck as they progress. For example:
25x to the 5th power take away x to the third power take away 8x take away 2x square divided by 5xsquare take away 4x. I have placed the dividend and divisor in descending order and even tried adding 0x to the fourth power in the dividend. I seem to get the first half correct, but can't get the latter half. What am I doing wrong?
Jennifer
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You have done the first steps correctly, that is you put the terms in decending order of degree and put a zero coefficient placeholder in for the missing 4th degree term. I presume you ended up with:

The next step is to factor the denominator. . Now your problem looks like this:

But notice that there is an in every term of the numerator which means you can divide through by the in the denominator to get:

Now your polynomial long division shouldn't be so ugly. I don't know how to render the process on this site, so I'll just talk you through it. Write back if you have trouble understanding.

Step 1: goes into times, so is the first term of your quotient polynomial.

Step 2: times is and times is , so is your first partial product.

Step 3: Subtract from the first two terms of the dividend polynomial giving you .

Step 4: Bring down the next term, to form your next partial dividend

Step 6: goes into times, so this is the next term of your quotient polynomial. So far, your quotient should look like .

Step 7: times is and times is , so is your next partial product.

Step 8: Subtract this from your previous partial dividend, (remembering to change the sign and add when you subtract), to get .

Step 9: Bring down the next term of the dividend, , to form your next partial dividend, .

Step 10: goes into times giving you the next term of your quotient. Your quotient should now look like .

Step 11: times is and times is , so is your next partial product.

Step 12: Subtract this from your previous partial dividend, , resulting in

Step 13: Bring down the last term, to form your next partial dividend

Step 14: goes into times, so is the last term of your quotient which should look like .

Step 15: times is and times is so your next partial product is .

Step 16: Subtract. . There is no remainder, so you are done.

Hope this helps.
John