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

Answer 1

#(x-1)/2#

#" "x^2+x-2# #color(magenta)(1/2x)(2x+4)->" "ul(x^2+2x) larr" subtract"# #" "0 -x-2# #color(magenta)(-1/2)(2x+4)->" "ul( -x-2) larr" subtract"# #" "0+0 larr" remainder"#

As the remainder is zero the division is exact.

#(x^2+x-2)/(2x+4)=color(magenta)( x/2-1/2)->(x-1)/2#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(brown)("The above is actually the same process as the traditional method.")##color(brown)("The only difference is the format chosen.")#
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Answer 2

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

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

      _______________________
    

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

  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 product (x) below the dividend, aligned with the x term.

      _______________________
    

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

  4. Subtract the product obtained in step 3 from the dividend. Write the result (-x - 2) below the line.

      _______________________
    

    2x + 4 | x^2 + x - 2 - (x^2 + 2x) _________________ -3x - 2

  5. Bring down the next term from the dividend, which is (-3x). Write it next to the result obtained in step 4.

      _______________________
    

    2x + 4 | x^2 + x - 2 - (x^2 + 2x) _________________ -3x - 2 - ( -3x - 6)

  6. Subtract the product obtained in step 5 from the result obtained in step 4. Write the result (4) below the line.

      _______________________
    

    2x + 4 | x^2 + x - 2 - (x^2 + 2x) _________________ -3x - 2 - ( -3x - 6) _________________ 4

  7. Since there are no more terms to bring down, the division is complete. The quotient is (1/2)x - 1 and the remainder is 4.

Therefore, (x^2+x-2)/(2x + 4) = (1/2)x - 1 + 4/(2x + 4).

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Answer 3

To divide ( \frac{x^2 + x - 2}{2x + 4} ) using polynomial long division, follow these steps:

  1. Divide the first term of the numerator by the first term of the denominator: ( \frac{x^2}{2x} = \frac{1}{2}x ).
  2. Multiply the entire denominator by ( \frac{1}{2}x ): ( \frac{1}{2}x \times (2x + 4) = x^2 + 2x ).
  3. Subtract the result from the numerator: ( (x^2 + x - 2) - (x^2 + 2x) = -x - 2 ).
  4. Bring down the next term from the numerator: ( -x - 2 ).
  5. Divide the leading term of the new polynomial by the first term of the denominator: ( \frac{-x}{2x} = -\frac{1}{2} ).
  6. Multiply the entire denominator by ( -\frac{1}{2} ): ( -\frac{1}{2} \times (2x + 4) = -x - 2 ).
  7. Subtract the result from the previous polynomial: ( (-x - 2) - (-x - 2) = 0 ).

The result of the division is ( \frac{1}{2}x - \frac{1}{2} ).

Therefore, ( \frac{x^2 + x - 2}{2x + 4} = \frac{1}{2}x - \frac{1}{2} ).

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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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