# How do you divide #(2x^3+9x^2-9x+1) / (2x-3) # using polynomial long division?

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To divide (2x^3+9x^2-9x+1) by (2x-3) using polynomial long division, follow these steps:

- Arrange the dividend (2x^3+9x^2-9x+1) and the divisor (2x-3) in descending order of exponents.
- Divide the first term of the dividend (2x^3) by the first term of the divisor (2x). The result is x^2.
- Multiply the divisor (2x-3) by the quotient obtained in step 2 (x^2). The result is 2x^3-3x^2.
- Subtract the product obtained in step 3 from the dividend. (2x^3+9x^2-9x+1) - (2x^3-3x^2) = 12x^2-9x+1.
- Bring down the next term from the dividend (-9x).
- Divide the first term of the new dividend (12x^2) by the first term of the divisor (2x). The result is 6x.
- Multiply the divisor (2x-3) by the quotient obtained in step 6 (6x). The result is 12x^2-18x.
- Subtract the product obtained in step 7 from the new dividend. (12x^2-9x+1) - (12x^2-18x) = 9x+1.
- Bring down the next term from the dividend (9x).
- Divide the first term of the new dividend (9x) by the first term of the divisor (2x). The result is 4.5.
- Multiply the divisor (2x-3) by the quotient obtained in step 10 (4.5). The result is 9x-13.5.
- Subtract the product obtained in step 11 from the new dividend. (9x+1) - (9x-13.5) = 14.5.
- There are no more terms to bring down, and the remainder (14.5) is less than the divisor (2x-3).
- The final quotient is x^2 + 6x + 4.5, and the remainder is 14.5.

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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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