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

The answer is

Let's divide something long.

Consequently,

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To divide (12x^4+12x^3-5x^2+9x+3) by (x^2-4), you can use long division. Here are the steps:

- Divide the first term of the numerator (12x^4) by the first term of the denominator (x^2). The result is 12x^2.
- Multiply the entire denominator (x^2-4) by the result from step 1 (12x^2), and subtract it from the numerator (12x^4+12x^3-5x^2+9x+3). This gives you: (12x^4+12x^3-5x^2+9x+3) - (12x^2 * (x^2-4)). Simplifying this expression gives: 12x^4+12x^3-5x^2+9x+3 - (12x^4-48x^2). Combining like terms gives: 12x^4+12x^3-5x^2+9x+3 - 12x^4+48x^2. Simplifying further gives: 12x^3+43x^2+9x+3.
- Repeat steps 1 and 2 with the simplified expression (12x^3+43x^2+9x+3) as the new numerator. Divide the first term of the new numerator (12x^3) by the first term of the denominator (x^2). The result is 12x. Multiply the entire denominator (x^2-4) by the result from step 3 (12x), and subtract it from the new numerator (12x^3+43x^2+9x+3). Simplify the expression obtained from the subtraction.
- Repeat steps 1 and 2 with the new simplified expression as the new numerator. Continue this process until you have divided all terms and no further division is possible.
- The final result will be the quotient obtained from the division.

Note: It is important to keep track of the powers of x and arrange the terms in descending order during the process.

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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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