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

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

- Arrange the dividend (x^3 - x^2 - 7x - 1) and the divisor (x+3) in descending order of powers of x.
- Divide the first term of the dividend (x^3) by the first term of the divisor (x). The result is x^2.
- Multiply the divisor (x+3) by the quotient obtained in step 2 (x^2). The result is (x^2)(x+3) = x^3 + 3x^2.
- Subtract the product obtained in step 3 from the dividend. (x^3 - x^2 - 7x - 1) - (x^3 + 3x^2) = -4x^2 - 7x - 1.
- Bring down the next term from the dividend, which is -4x^2.
- Divide the first term of the new dividend (-4x^2) by the first term of the divisor (x). The result is -4x.
- Multiply the divisor (x+3) by the quotient obtained in step 6 (-4x). The result is (-4x)(x+3) = -4x^2 - 12x.
- Subtract the product obtained in step 7 from the new dividend. (-4x^2 - 7x - 1) - (-4x^2 - 12x) = 5x - 1.
- Bring down the next term from the dividend, which is 5x.
- Divide the first term of the new dividend (5x) by the first term of the divisor (x). The result is 5.
- Multiply the divisor (x+3) by the quotient obtained in step 10 (5). The result is (5)(x+3) = 5x + 15.
- Subtract the product obtained in step 11 from the new dividend. (5x - 1) - (5x + 15) = -16.
- Since there are no more terms in the dividend, the division is complete.
- The quotient is x^2 - 4x + 5, and the remainder is -16.

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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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