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

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Using

Using

Long divide the coefficients to find:

#(x^4+2x^3+3x-1)/(x^2+2) = x^2+2x-2+(-x+3)/(x^2+2)#

I like to long divide the coefficients, not forgetting to include

This is similar to long division of numbers.

Write the dividend

Write the first term

Write the product

Write the second term

Write the product

Write the third term

Write the product

This is where we stop, since the running remainder is now shorter than the divisor and there are no more terms to bring down from the dividend.

The resulting quotient is

So:

#(x^4+2x^3+3x-1)/(x^2+2) = x^2+2x-2+(-x+3)/(x^2+2)#

Or if you prefer:

#x^4+2x^3+3x-1#

#= (x^2+2)(x^2+2x-2) + (-x+3)#

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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 as the first term of the quotient.

Next, multiply the entire denominator (x^2 + 2) by the first term of the quotient (x^2), and subtract the result from the numerator (x^4 + 2x^3 + 3x - 1).

This gives you a new polynomial to divide. Repeat the process by dividing the highest degree term of the new polynomial by the highest degree term of the denominator.

Continue this process until you have divided all the terms of the numerator. The final result will be the quotient.

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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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