How do you divide #(x^2+x1)/(2x + 4)# using polynomial long division?
We divide polynomials just like we are dividing integers
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To divide (x^2+x1) by (2x + 4) using polynomial long division, follow these steps:

Write the dividend (x^2+x1) and the divisor (2x + 4) in the long division format.
_______________________
2x + 4  x^2 + x  1

Divide the first term of the dividend (x^2) by the first term of the divisor (2x). The result is (1/2)x.

Multiply the divisor (2x + 4) by the result obtained in step 2, which is (1/2)x. Write the result below the dividend, aligning like terms.
(1/2)x _______________________
2x + 4  x^2 + x  1  (x^2 + 2x)

Subtract the result obtained in step 3 from the dividend. Write the result below the line.
(1/2)x _______________________
2x + 4  x^2 + x  1  (x^2 + 2x) _______________ x  1

Bring down the next term from the dividend, which is 1.
(1/2)x _______________________
2x + 4  x^2 + x  1  (x^2 + 2x) _______________ x  1  (1)

Divide the new dividend (x  1) by the first term of the divisor (2x). The result is (1/2).

Multiply the divisor (2x + 4) by the result obtained in step 6, which is (1/2). Write the result below the line.
(1/2)x  (1/2) _______________________
2x + 4  x^2 + x  1  (x^2 + 2x) _______________ x  1  (x  2)

Subtract the result obtained in step 7 from the previous result. Write the result below the line.
(1/2)x  (1/2) _______________________
2x + 4  x^2 + x  1  (x^2 + 2x) _______________ x  1  (x  2) _______________ 1

The remainder is 1. Since there are no more terms to bring down, the division is complete.

The final result of the division is (1/2)x  (1/2) with a remainder of 1.
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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.
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