# How do you divide #( x^3+4x^2-17x-16 )/(x-4)#?

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To divide (x^3+4x^2-17x-16) by (x-4), you can use long division. Here are the steps:

- Divide the first term of the numerator (x^3) by the first term of the denominator (x). This gives x^2.
- Multiply the entire denominator (x-4) by the result from step 1 (x^2), and subtract it from the numerator (x^3+4x^2-17x-16). This gives (x^3+4x^2-17x-16) - (x^2 * (x-4)). Simplifying, we get (x^3+4x^2-17x-16) - (x^3-4x^2). This further simplifies to 8x^2-17x-16.
- Repeat steps 1 and 2 with the simplified numerator (8x^2-17x-16). Divide the first term (8x^2) by the first term of the denominator (x), giving 8x. Multiply the entire denominator (x-4) by the result from step 3 (8x), and subtract it from the simplified numerator (8x^2-17x-16). This gives (8x^2-17x-16) - (8x * (x-4)). Simplifying, we get (8x^2-17x-16) - (8x^2-32x). This further simplifies to 15x-16.
- Repeat steps 1 and 2 with the new simplified numerator (15x-16). Divide the first term (15x) by the first term of the denominator (x), giving 15. Multiply the entire denominator (x-4) by the result from step 4 (15), and subtract it from the simplified numerator (15x-16). This gives (15x-16) - (15 * (x-4)). Simplifying, we get (15x-16) - (15x-60). This further simplifies to 44.
- Since there are no more terms left in the numerator, the division is complete. The quotient is x^2 + 8x + 15, and the remainder is 44.

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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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