# How do you divide #(5x^4+2x^3-9x+12)/(x^2-3x+4)#?

you have to do long division,

Here is my best attempt at the answer and I hope it's right, because I worked for a very long time to draw it out on paint. If it is not correct, I am sure the setup is correct, so you can use it to repeat the calculation for new problems.

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To divide (5x^4+2x^3-9x+12) by (x^2-3x+4), you can use long division or synthetic division. Here is the step-by-step process using long division:

- Divide the first term of the numerator (5x^4) by the first term of the denominator (x^2). The result is 5x^2.
- Multiply the entire denominator (x^2-3x+4) by the result from step 1 (5x^2), and subtract it from the numerator (5x^4+2x^3-9x+12). This gives you (5x^4+2x^3-9x+12) - (5x^2 * (x^2-3x+4)). Simplifying further, you get 2x^3-9x+12 - (5x^4-15x^3+20x^2).
- Bring down the next term from the numerator, which is -15x^3.
- Divide the first term of the new expression (-15x^3) by the first term of the denominator (x^2). The result is -15x.
- Multiply the entire denominator (x^2-3x+4) by the result from step 4 (-15x), and subtract it from the new expression. This gives you -15x^3 + 2x^3 - 9x + 12 - (-15x * (x^2-3x+4)). Simplifying further, you get -15x^3 + 2x^3 - 9x + 12 - (-15x^3 + 45x^2 - 60x).
- Continue this process until you have divided all the terms. The final result will be the quotient.

The quotient of (5x^4+2x^3-9x+12)/(x^2-3x+4) is 5x^2 - 15x + 3, with a remainder of (-60x + 12)/(x^2-3x+4).

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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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