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

We can lessen the dividend and divisor's degree.

the common monomial x as a factor

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

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

- Divide the first term of the numerator (x^4) by the first term of the denominator (x) to get x^3.
- Multiply x^3 by the entire denominator (x(x+4)) to get x^3(x+4) = x^4 + 4x^3.
- Subtract this result (x^4 + 4x^3) from the numerator (x^4-2x^3-x) to get -6x^3-x.
- Bring down the next term (-6x^3) and repeat the process.
- Divide the first term of the new numerator (-6x^3) by the first term of the denominator (x) to get -6x^2.
- Multiply -6x^2 by the entire denominator (x(x+4)) to get -6x^2(x+4) = -6x^3 - 24x^2.
- Subtract this result (-6x^3 - 24x^2) from the new numerator (-6x^3-x) to get 24x^2-x.
- Bring down the next term (24x^2) and repeat the process.
- Divide the first term of the new numerator (24x^2) by the first term of the denominator (x) to get 24x.
- Multiply 24x by the entire denominator (x(x+4)) to get 24x(x+4) = 24x^2 + 96x.
- Subtract this result (24x^2 + 96x) from the new numerator (24x^2-x) to get -97x.
- Bring down the next term (-97x) and repeat the process.
- Divide the first term of the new numerator (-97x) by the first term of the denominator (x) to get -97.
- Multiply -97 by the entire denominator (x(x+4)) to get -97(x+4) = -97x - 388.
- Subtract this result (-97x - 388) from the new numerator (-97x) to get -388.
- 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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