# How do you divide #( x^3 + 2x^2 – 3x – 5)/(x - 2 )#?

Using the divisor x - 2 as a factor in the numerator is one method.

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To divide (x^3 + 2x^2 – 3x – 5) by (x - 2), 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 - 2) by the result from step 1 (x^2), and subtract it from the numerator (x^3 + 2x^2 – 3x – 5). This gives (x^3 + 2x^2 – 3x – 5) - (x^2 * (x - 2)). Simplifying, we get (x^3 + 2x^2 – 3x – 5) - (x^3 - 2x^2). This further simplifies to (x^3 + 2x^2 – 3x – 5 - x^3 + 2x^2). Combining like terms, we have 4x^2 – 3x – 5.
- Repeat steps 1 and 2 with the simplified numerator (4x^2 – 3x – 5) and the denominator (x - 2). Divide the first term of the simplified numerator (4x^2) by the first term of the denominator (x). This gives 4x. Multiply the entire denominator (x - 2) by the result from step 3 (4x), and subtract it from the simplified numerator (4x^2 – 3x – 5). Simplifying, we get (4x^2 – 3x – 5) - (4x * (x - 2)). Expanding, we have (4x^2 – 3x – 5) - (4x^2 - 8x). This simplifies to (4x^2 – 3x – 5 - 4x^2 + 8x). Combining like terms, we obtain 5x - 5.
- The result of the division is the quotient obtained from step 1 (x^2) plus the quotient obtained from step 3 (4x), which gives the final answer: x^2 + 4x.

Therefore, (x^3 + 2x^2 – 3x – 5)/(x - 2) = x^2 + 4x.

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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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