# For example, f(x) is a multipart which if divided by #x^3+27#, the remainder is #x^2-2x+7#. If f(x) is divided by #x^2-3x+9#, the remainder is?

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To find the remainder when ( f(x) ) is divided by ( x^2 - 3x + 9 ), we can use polynomial long division or synthetic division.

Given that the remainder when ( f(x) ) is divided by ( x^3 + 27 ) is ( x^2 - 2x + 7 ), we can express ( f(x) ) as:

[ f(x) = q(x) \cdot (x^3 + 27) + (x^2 - 2x + 7) ]

Now, we need to express ( x^2 - 2x + 7 ) in terms of ( x^2 - 3x + 9 ) to find the remainder.

We can rewrite ( x^2 - 2x + 7 ) as:

[ x^2 - 2x + 7 = (x^2 - 3x + 9) - (x - 2) ]

So, we have:

[ f(x) = q(x) \cdot (x^3 + 27) + (x^2 - 3x + 9) - (x - 2) ]

Now, when ( f(x) ) is divided by ( x^2 - 3x + 9 ), the remainder is ( x - 2 ).

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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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