# How do you divide #( -2x^4 + x^3 + x^2 +14x)/(x^2+4)#?

Solve using polynomial long division:

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To divide (-2x^4 + x^3 + x^2 + 14x) by (x^2 + 4), you can use long division. Here are the steps:

- Divide the first term of the numerator (-2x^4) by the first term of the denominator (x^2). The result is -2x^2.
- Multiply the entire denominator (x^2 + 4) by -2x^2, giving -2x^4 - 8x^2.
- Subtract this result from the numerator (-2x^4 + x^3 + x^2 + 14x) to get (x^3 + 9x^2 + 14x).
- Bring down the next term from the numerator, which is x^2.
- Divide the first term of the new numerator (x^3) by the first term of the denominator (x^2). The result is x.
- Multiply the entire denominator (x^2 + 4) by x, giving x^3 + 4x.
- Subtract this result from the new numerator (x^3 + 9x^2 + 14x) to get (5x^2 + 14x).
- Bring down the next term from the numerator, which is 14x.
- Divide the first term of the new numerator (5x^2) by the first term of the denominator (x^2). The result is 5.
- Multiply the entire denominator (x^2 + 4) by 5, giving 5x^2 + 20.
- Subtract this result from the new numerator (5x^2 + 14x) to get (-6x).
- There are no more terms left in the numerator, so the division is complete.

The final result of the division is: -2x^2 + x + 5, with a remainder of -6x.

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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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