# How do you divide #(x^3-7x^2+17x+13 ) / (2x+1) # using polynomial long division?

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To divide (x^3-7x^2+17x+13) by (2x+1) using polynomial long division, follow these steps:

- Arrange the dividend (x^3-7x^2+17x+13) and the divisor (2x+1) in descending order of powers of x.
- Divide the first term of the dividend (x^3) by the first term of the divisor (2x). The result is (1/2)x^2.
- Multiply the divisor (2x+1) by the result obtained in step 2, which is (1/2)x^2. The product is (1/2)x^3 + (1/2)x^2.
- Subtract the product obtained in step 3 from the dividend. (x^3-7x^2+17x+13) - ((1/2)x^3 + (1/2)x^2) = (-9/2)x^2 + 17x + 13.
- Bring down the next term from the dividend, which is 17x.
- Divide the first term of the new dividend (-9/2)x^2 by the first term of the divisor (2x). The result is (-9/4)x.
- Multiply the divisor (2x+1) by the result obtained in step 6, which is (-9/4)x. The product is (-9/4)x^2 - (9/4)x.
- Subtract the product obtained in step 7 from the new dividend. (-9/2)x^2 + 17x + 13 - ((-9/4)x^2 - (9/4)x) = (49/4)x + 13.
- Bring down the next term from the dividend, which is 13.
- Divide the first term of the new dividend (49/4)x by the first term of the divisor (2x). The result is (49/8).
- Multiply the divisor (2x+1) by the result obtained in step 10, which is (49/8). The product is (49/4)x + (49/8).
- Subtract the product obtained in step 11 from the new dividend. (49/4)x + 13 - ((49/4)x + (49/8)) = (91/8).
- There are no more terms left in the dividend, so the division is complete.
- The quotient is (1/2)x^2 - (9/4)x + (49/8) and the remainder is (91/8).

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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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