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
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