# How do you divide: #(x^3 - 6x^2 + 12x - 8) ÷ (x - 2)#?

Another way to solve this problem is to factor the dividend polynomial to see if there are any factors which are the divisor!

In fact it is - and we can use the intermediate result in red above to find the answer to our question:

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To divide (x^3 - 6x^2 + 12x - 8) by (x - 2), you can use long division. Here are the steps:

- Divide the first term of the dividend (x^3) by the divisor (x). This gives x^2.
- Multiply the divisor (x - 2) by the quotient obtained in step 1 (x^2). This gives (x^2 - 2x).
- Subtract the result obtained in step 2 from the dividend (x^3 - 6x^2 + 12x - 8) to get the new dividend: (-4x^2 + 12x - 8).
- Repeat steps 1-3 with the new dividend (-4x^2 + 12x - 8).
- Divide the first term of the new dividend (-4x^2) by the divisor (x). This gives -4x.
- Multiply the divisor (x - 2) by the quotient obtained in step 4 (-4x). This gives (-4x^2 + 8x).
- Subtract the result obtained in step 4 from the new dividend (-4x^2 + 12x - 8) to get the new dividend: (4x - 8).

- Repeat steps 1-3 with the new dividend (4x - 8).
- Divide the first term of the new dividend (4x) by the divisor (x). This gives 4.
- Multiply the divisor (x - 2) by the quotient obtained in step 5 (4). This gives (4x - 8).
- Subtract the result obtained in step 5 from the new dividend (4x - 8) to get the remainder: 0.

The quotient is x^2 - 4x + 4, and there is no remainder.

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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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