How do you divide #(x^4+2x^32x^2+9x+3)/(x^2+1) #?
Through extensive division
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To divide (x^4+2x^32x^2+9x+3) by (x^2+1), you can use long division. Here are the steps:

Divide the first term of the numerator (x^4) by the first term of the denominator (x^2). The result is x^2.

Multiply the entire denominator (x^2+1) by the result from step 1 (x^2). This gives you x^4+x^2.

Subtract the result from step 2 (x^4+x^2) from the numerator (x^4+2x^32x^2+9x+3). This gives you (2x^33x^2+9x+3).

Bring down the next term from the numerator, which is 0x. Now you have (2x^33x^2+9x+3).

Divide the first term of the new numerator (2x^3) by the first term of the denominator (x^2). The result is 2x.

Multiply the entire denominator (x^2+1) by the result from step 5 (2x). This gives you 2x^3+2x.

Subtract the result from step 6 (2x^3+2x) from the new numerator (2x^33x^2+9x+3). This gives you (3x^2+9x+3).

Repeat steps 47 until you have no more terms to bring down.
In this case, the division will continue indefinitely, as the degree of the numerator is greater than the degree of the denominator. Therefore, the division is not possible in this case.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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