# How do you divide #(x-5x^2+10+x^3)/(x+2)#?

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To divide (x-5x^2+10+x^3) by (x+2), you can use long division. Here are the steps:

- Divide the first term of the numerator (x^3) by the first term of the denominator (x). This gives x^2.
- Multiply the entire denominator (x+2) by the quotient obtained in step 1 (x^2). This gives x^3+2x^2.
- Subtract the result obtained in step 2 from the numerator (x-5x^2+10+x^3). This gives -7x^2+10.
- Bring down the next term from the numerator (-7x^2+10), which is -7x^2.
- Divide the first term of the new numerator (-7x^2) by the first term of the denominator (x). This gives -7x.
- Multiply the entire denominator (x+2) by the quotient obtained in step 5 (-7x). This gives -7x^2-14x.
- Subtract the result obtained in step 6 from the new numerator (-7x^2+10). This gives 24x+10.
- Bring down the next term from the numerator (24x+10), which is 24x.
- Divide the first term of the new numerator (24x) by the first term of the denominator (x). This gives 24.
- Multiply the entire denominator (x+2) by the quotient obtained in step 9 (24). This gives 24x+48.
- Subtract the result obtained in step 10 from the new numerator (24x+10). This gives -38.
- There are no more terms left in the numerator, so the division is complete.

The quotient is x^2 - 7x + 24, and the remainder is -38.

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To divide ( \frac{x - 5x^2 + 10 + x^3}{x + 2} ), you can use polynomial long division or synthetic division. Let's use polynomial long division.

- Divide the first term of the numerator by the first term of the denominator.
- Multiply the entire denominator by the quotient obtained in step 1.
- Subtract the result obtained in step 2 from the numerator.
- Repeat steps 1-3 until you obtain a remainder with degree less than the denominator.

Following these steps, the division yields a quotient of ( x^2 - 5x + 10 ) and a remainder of ( -20 ).

Therefore, ( \frac{x - 5x^2 + 10 + x^3}{x + 2} = x^2 - 5x + 10 - \frac{20}{x + 2} ).

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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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