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

Answer 1

Long divide the coefficients to find:

#(x^4-2x^3-2x^2-2x+3)/(x^2-3) = x^2-2x+1+(-8x+6)/(x^2-3)#

I like to long divide the coefficients like this:

Note that the divisor is written #1, 0, -3#, including a #0# for the coefficient of the term in #x#.

Write the dividend under the bar and the divisor to the left.

Write the quotient term-by-term above the bar, choosing each digit so that when multiplied by the divisor it matches the leading term of your running remainder. Once the remainder is too short to allow further division, you are finished.

The quotient represented by #1, -2, 1# is #x^2-2x+1# and the remainder #-8x+6#

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Answer 2

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

  1. Divide the first term of the numerator (x^4) by the first term of the denominator (x^2). The result is x^2.

  2. Multiply the entire denominator (x^2-3) by the result from step 1 (x^2). This gives you x^4-3x^2.

  3. Subtract the result from step 2 (x^4-3x^2) from the numerator (x^4-2x^3-2x^2-2x+3). This gives you (-2x^3+2x^2-2x+3).

  4. Bring down the next term from the numerator (-2x^3).

  5. Divide the first term of the new numerator (-2x^3) by the first term of the denominator (x^2). The result is -2x.

  6. Multiply the entire denominator (x^2-3) by the result from step 5 (-2x). This gives you -2x^3+6x.

  7. Subtract the result from step 6 (-2x^3+6x) from the new numerator (-2x^3+2x^2-2x+3). This gives you (-2x^2-8x+3).

  8. Bring down the next term from the numerator (-2x^2).

  9. Divide the first term of the new numerator (-2x^2) by the first term of the denominator (x^2). The result is -2.

  10. Multiply the entire denominator (x^2-3) by the result from step 9 (-2). This gives you -2x^2+6.

  11. Subtract the result from step 10 (-2x^2+6) from the new numerator (-2x^2-8x+3). This gives you (-8x-3).

  12. Bring down the next term from the numerator (-8x).

  13. Divide the first term of the new numerator (-8x) by the first term of the denominator (x^2). The result is -8x.

  14. Multiply the entire denominator (x^2-3) by the result from step 13 (-8x). This gives you -8x^2+24x.

  15. Subtract the result from step 14 (-8x^2+24x) from the new numerator (-8x-3). This gives you (24x-3).

  16. Bring down the next term from the numerator (24x).

  17. Divide the first term of the new numerator (24x) by the first term of the denominator (x^2). The result is 24x.

  18. Multiply the entire denominator (x^2-3) by the result from step 17 (24x). This gives you 24x^2-72.

  19. Subtract the result from step 18 (24x^2-72) from the new numerator (24x-3). This gives you (75).

  20. Since the degree of the new numerator (75) is less than the degree of the denominator (x^2-3), the division is complete.

Therefore, the result of the division is (x^2-2) with a remainder of 75.

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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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