SOLUTION: use polynomial long division to divide 4x^3+x^2+17x-15 by -x^2-x-5. Please show all work! Thank you

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Question 474995: use polynomial long division to divide 4x^3+x^2+17x-15 by -x^2-x-5. Please show all work! Thank you
Answer by karaoz(32) About Me  (Show Source):
You can put this solution on YOUR website!
  4x3 +  x2 + 17x - 15 : -x2 - x - 5
We will call the first expression "dividend" and the second "divisor".
First thing to do is to look at the first term of both expressions,
4x3 and -x2, and answer the question
"How much is (4x3)/(-x2)?"
This answer, which is -4x, is the first term of the result. Hence, 1st step is:
  4x3 +  x2 + 17x - 15 : -x2 - x - 5 = -4x ...
Next thing to do is to multiply divisor by this term just obtained (-4x) and write the result immediately below the dividend aligning the like terms below each other.
  4x3 +  x2 + 17x - 15 : -x2 - x - 5 = -4x ...
  4x3 + 4x2 + 20x
Now, subtract the obtained product from the dividend and write the result immediately below... like this:
  4x3 +  x2 + 17x - 15 : -x2 - x - 5 = -4x ...
-(4x3 + 4x2 + 20x)
----------------------
      - 3x2 -  3x - 15
The last line basically shows what is left after the product between the divisor and the temporary result (-4x) is taken away from the dividend.
The rest of the process repeats itself, with the new line being your new dividend.
So, the question is then "What is (-3x2)/(-x2) and the answer should be 3. So, the next term to add to our temporary result is simply 3.
4x3 +  x2 + 17x - 15 : -x2 - x - 5 = -4x + 3 ...
So, using the same principles, we now multiply this new result (3) by the divisor and write the result immediately below the new dividend.
  4x3 +  x2 + 17x - 15 : -x2 - x - 5 = -4x + 3 ...
-(4x3 + 4x2 + 20x)
----------------------
      - 3x2 -  3x - 15
      - 3x2 -  3x - 15
Subtract the result obtained from the new dividend and write the result immediately below. This will get us:
  4x3 +  x2 + 17x - 15 : -x2 - x - 5 = -4x + 3 ...
-(4x3 + 4x2 + 20x)
----------------------
      - 3x2 -  3x - 15
    -(- 3x2 -  3x - 15)
----------------------
                     0
This means that when the product between (-4x + 3) and the divisor is taken away from the original dividend, we are left with 0. So, this clearly means that:
4x3 +  x2 + 17x - 15 = (-x2 - x - 5)(-4x + 3).
We have the result (-4x + 3) and the complete process of obtaining this result is shown once again:
  4x3 +  x2 + 17x - 15 : -x2 - x - 5 = -4x + 3
-(4x3 + 4x2 + 20x)
----------------------
      - 3x2 -  3x - 15
    -(- 3x2 -  3x - 15)
----------------------
                     0