How do you divide #(-x^4+6x^3-12x^2-7x-7)/(x-2) #?

Answer 1

To simplify the given equation, divide the number values and subtract the variable's exponent. (see explanation)

#(-x^4+6x^3-12x^2-7x-7)/(x-2)# #=(-x^3-3x^2+6x)+(7/2)+(7/2)# #=-x^3-3x^2+6x+7#
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Answer 2

To divide (-x^4+6x^3-12x^2-7x-7) by (x-2), you can use long division. Here are the steps:

  1. Divide the first term of the numerator (-x^4) by the first term of the denominator (x). The result is -x^3.
  2. Multiply the entire denominator (x-2) by -x^3, giving -x^4+2x^3.
  3. Subtract this result (-x^4+2x^3) from the original numerator (-x^4+6x^3-12x^2-7x-7). The subtraction gives 4x^3-12x^2-7x-7.
  4. Bring down the next term from the numerator, which is -12x^2.
  5. Divide -12x^2 by x, giving -12x.
  6. Multiply the entire denominator (x-2) by -12x, resulting in -12x^2+24x.
  7. Subtract this result (-12x^2+24x) from the previous result (4x^3-12x^2-7x-7). The subtraction gives 4x^3-36x-7x-7.
  8. Bring down the next term from the numerator, which is -7x.
  9. Divide -7x by x, giving -7.
  10. Multiply the entire denominator (x-2) by -7, resulting in -7x+14.
  11. Subtract this result (-7x+14) from the previous result (4x^3-36x-7x-7). The subtraction gives 4x^3-43x-21.
  12. Bring down the last term from the numerator, which is -7.
  13. Divide -7 by x, giving -7/x.
  14. Multiply the entire denominator (x-2) by -7/x, resulting in -7+14/x.
  15. Subtract this result (-7+14/x) from the previous result (4x^3-43x-21). The subtraction gives 4x^3-43x-21-(-7+14/x).

The final result of the division is 4x^3-43x-21-(-7+14/x).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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