How do you divide #(x^2+x-1)/(2x + 4)# using polynomial long division?

Answer 1

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

We divide polynomials just like we are dividing integers

#" " " " " " " "underline(1/2x-1/2 " " " " "larr )#the quotient #2x+4" "|~x^2+x-1# #" " " " " " " "underline(x^2+2x" " " " " " ")# #" " " " " " " " " "-x-1# #" " " " " " " " " "underline(-x-2 " " " " ")# #" " " " " " " " " " " " " "+1 larr "remainder"#

Our final answer will be written

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

God bless....I hope the explanation is useful.

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Answer 2

To divide (x^2+x-1) by (2x + 4) using polynomial long division, follow these steps:

  1. Write the dividend (x^2+x-1) and the divisor (2x + 4) in the long division format.

      _______________________
    

    2x + 4 | x^2 + x - 1

  2. Divide the first term of the dividend (x^2) by the first term of the divisor (2x). The result is (1/2)x.

  3. Multiply the divisor (2x + 4) by the result obtained in step 2, which is (1/2)x. Write the result below the dividend, aligning like terms.

      (1/2)x
      _______________________
    

    2x + 4 | x^2 + x - 1 - (x^2 + 2x)

  4. Subtract the result obtained in step 3 from the dividend. Write the result below the line.

      (1/2)x
      _______________________
    

    2x + 4 | x^2 + x - 1 - (x^2 + 2x) _______________ -x - 1

  5. Bring down the next term from the dividend, which is -1.

      (1/2)x
      _______________________
    

    2x + 4 | x^2 + x - 1 - (x^2 + 2x) _______________ -x - 1 - (-1)

  6. Divide the new dividend (-x - 1) by the first term of the divisor (2x). The result is (-1/2).

  7. Multiply the divisor (2x + 4) by the result obtained in step 6, which is (-1/2). Write the result below the line.

      (1/2)x - (1/2)
      _______________________
    

    2x + 4 | x^2 + x - 1 - (x^2 + 2x) _______________ -x - 1 - (-x - 2)

  8. Subtract the result obtained in step 7 from the previous result. Write the result below the line.

      (1/2)x - (1/2)
      _______________________
    

    2x + 4 | x^2 + x - 1 - (x^2 + 2x) _______________ -x - 1 - (-x - 2) _______________ 1

  9. The remainder is 1. Since there are no more terms to bring down, the division is complete.

  10. The final result of the division is (1/2)x - (1/2) with a remainder of 1.

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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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