# How do you divide #(2x^3 - 6x^2 + 8) / (x^2 - 4)#?

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To divide (2x^3 - 6x^2 + 8) by (x^2 - 4), we can use polynomial long division.

First, we divide the highest degree term of the numerator (2x^3) by the highest degree term of the denominator (x^2). This gives us 2x as the quotient.

Next, we multiply the entire denominator (x^2 - 4) by the quotient (2x), which gives us 2x(x^2 - 4) = 2x^3 - 8x.

We then subtract this result from the numerator (2x^3 - 6x^2 + 8) to get the remainder: (2x^3 - 6x^2 + 8) - (2x^3 - 8x) = -6x^2 + 8x + 8.

Now, we repeat the process with the remainder (-6x^2 + 8x + 8) and the denominator (x^2 - 4).

We divide the highest degree term of the remainder (-6x^2) by the highest degree term of the denominator (x^2), which gives us -6x as the quotient.

We multiply the entire denominator (x^2 - 4) by the quotient (-6x), which gives us -6x(x^2 - 4) = -6x^3 + 24x.

We subtract this result from the remainder (-6x^2 + 8x + 8) to get the new remainder: (-6x^2 + 8x + 8) - (-6x^3 + 24x) = 6x^3 - 14x + 8.

Since the degree of the new remainder (6x^3 - 14x + 8) is less than the degree of the denominator (x^2 - 4), we have reached the end of the division.

Therefore, the quotient is 2x - 6x and the remainder is 6x^3 - 14x + 8.

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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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