# How do you divide #(x^4 + 2x^3 +3x -1) /(x^2+2)#?

Using the distribution method, you can expand the expression.

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To divide (x^4 + 2x^3 + 3x - 1) by (x^2 + 2), you can use long division.

First, divide the highest degree term of the numerator (x^4) by the highest degree term of the denominator (x^2). This gives x^2.

Next, multiply the entire denominator (x^2 + 2) by the result from the previous step (x^2), and subtract the result from the numerator (x^4 + 2x^3 + 3x - 1). This gives you a new polynomial: (2x^3 + 3x - 1 - x^2(x^2 + 2)). Simplifying further, you get (2x^3 + 3x - 1 - x^4 - 2x^2).

Repeat the process by dividing the highest degree term of the new polynomial (2x^3) by the highest degree term of the denominator (x^2). This gives you 2x.

Multiply the entire denominator (x^2 + 2) by the result from the previous step (2x), and subtract the result from the new polynomial (2x^3 + 3x - 1 - 2x(x^2 + 2)). Simplifying further, you get (3x - 1 - 2x^3 - 4x).

Continue this process until you have no more terms to divide. In this case, the final result is (x^2 + 2x - 1).

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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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