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

Answer 1

#(x^4-2x^3-x)/(x(x+4))=(x^3-2x^2-1)/(x+4)=color(red)(x^2-6x+24-97/(x+4))#

From the given #(x^4-2x^3-x)/(x(x+4))#

We can lessen the dividend and divisor's degree.

#(x^4-2x^3-x)/(x(x+4))#

the common monomial x as a factor

#(x(x^3-2x^2-1))/(x(x+4))#
#(cancelx(x^3-2x^2-1))/(cancelx(x+4))#
#(x^3-2x^2-1)/(x+4)#
Perform long division #" " " " ""underline(x^2-6x+24" " " " " ")# #x+4|~x^3-2x^2+0*x-1# #"" " " " " underline(x^3+4x^2" " " " "" " " " "" " " " ")# #" " " " " " " "-6x^2+0*x-1# #" " " " " " " "underline(-6x^2-24x" " " " "" " " " ")# #" " " " " " " " " " " " " " "24x-1# #" " " " " " " " " " " " " " "underline(24x+96)# #" " " " " " " " " " " " " " " " " " -97##larr#remainder

This is how we write our response.

#("Dividend")/("Divisor")="Quotient"+("Remainder")/("Divisor")#
#(x^4-2x^3-x)/(x(x+4))=x^2-6x+24-97/(x+4)#

May God bless you all. I hope this explanation helps.

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Answer 2

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

  1. Divide the first term of the numerator (x^4) by the first term of the denominator (x) to get x^3.
  2. Multiply x^3 by the entire denominator (x(x+4)) to get x^3(x+4) = x^4 + 4x^3.
  3. Subtract this result (x^4 + 4x^3) from the numerator (x^4-2x^3-x) to get -6x^3-x.
  4. Bring down the next term (-6x^3) and repeat the process.
  5. Divide the first term of the new numerator (-6x^3) by the first term of the denominator (x) to get -6x^2.
  6. Multiply -6x^2 by the entire denominator (x(x+4)) to get -6x^2(x+4) = -6x^3 - 24x^2.
  7. Subtract this result (-6x^3 - 24x^2) from the new numerator (-6x^3-x) to get 24x^2-x.
  8. Bring down the next term (24x^2) and repeat the process.
  9. Divide the first term of the new numerator (24x^2) by the first term of the denominator (x) to get 24x.
  10. Multiply 24x by the entire denominator (x(x+4)) to get 24x(x+4) = 24x^2 + 96x.
  11. Subtract this result (24x^2 + 96x) from the new numerator (24x^2-x) to get -97x.
  12. Bring down the next term (-97x) and repeat the process.
  13. Divide the first term of the new numerator (-97x) by the first term of the denominator (x) to get -97.
  14. Multiply -97 by the entire denominator (x(x+4)) to get -97(x+4) = -97x - 388.
  15. Subtract this result (-97x - 388) from the new numerator (-97x) to get -388.
  16. There are no more terms to bring down, so the division is complete.

The quotient is x^3 - 6x^2 + 24x - 97, and the remainder is -388.

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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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