How do you divide #(4x^4 -12 x^2-x-20)/((x^2 + 4) )#?
The quotient is
Make a lengthy division.
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To divide (4x^4 - 12x^2 - x - 20) by (x^2 + 4), you can use long division. Here are the steps:
- Divide the first term of the numerator (4x^4) by the first term of the denominator (x^2). This gives you 4x^2.
- Multiply the entire denominator (x^2 + 4) by the result from step 1 (4x^2). This gives you 4x^4 + 16x^2.
- Subtract the result from step 2 from the numerator (4x^4 - 12x^2 - x - 20) to get the remainder: -28x^2 - x - 20.
- Bring down the next term from the numerator (-28x^2) and divide it by the first term of the denominator (x^2). This gives you -28.
- Multiply the entire denominator (x^2 + 4) by the result from step 4 (-28). This gives you -28x^2 - 112.
- Subtract the result from step 5 from the remainder (-28x^2 - x - 20) to get the new remainder: 111.
- Bring down the next term from the numerator (111) and divide it by the first term of the denominator (x^2). This gives you 111x^0, which is simply 111.
- Multiply the entire denominator (x^2 + 4) by the result from step 7 (111). This gives you 111x^2 + 444.
- Subtract the result from step 8 from the new remainder (111) to get the final remainder: -333.
Therefore, the division of (4x^4 - 12x^2 - x - 20) by (x^2 + 4) is equal to 4x^2 - 28 + 111/(x^2 + 4) with a remainder of -333.
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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.
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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