How do you divide #(4x^4 -12 x^2-x-20)/((x^2 + 4) )#?

Answer 1

The quotient is #(4x^2-28)# and the remainder is #(-x+92)#

Make a lengthy division.

#color(white)(aaaa)##4x^4-12x^2-x-20##color(white)(aaaa)##|##x^2+4#
#color(white)(aaaa)##4x^4+16x^2##color(white)(aaaaaaaaaaaa)##|##4x^2-28#
#color(white)(aaaaaa)##0-28x^2-x-20#
#color(white)(aaaaaaaa)##-28x^2-0x-112#
#color(white)(aaaaaaaaaa)##+0-x+92#
The quotient is #(4x^2-28)# and the remainder is #(-x+92)#
#(4x^4-12x^2-x-20)/(x^2+4)=4x^2-28+(-x+92)/(x^2+4)#
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Answer 2

To divide (4x^4 - 12x^2 - x - 20) by (x^2 + 4), you can use long division. Here are the steps:

  1. Divide the first term of the numerator (4x^4) by the first term of the denominator (x^2). This gives you 4x^2.
  2. Multiply the entire denominator (x^2 + 4) by the result from step 1 (4x^2). This gives you 4x^4 + 16x^2.
  3. Subtract the result from step 2 from the numerator (4x^4 - 12x^2 - x - 20) to get the remainder: -28x^2 - x - 20.
  4. 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.
  5. Multiply the entire denominator (x^2 + 4) by the result from step 4 (-28). This gives you -28x^2 - 112.
  6. Subtract the result from step 5 from the remainder (-28x^2 - x - 20) to get the new remainder: 111.
  7. 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.
  8. Multiply the entire denominator (x^2 + 4) by the result from step 7 (111). This gives you 111x^2 + 444.
  9. 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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Answer from HIX Tutor

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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