The table represents the start of the division of 8x^4+2x^3-7x^2+3x-2 by the indicated divisor. Find the quotient.

Answer: 2x² + x - 2 (the first option)

Explanation:

1) Question: divide 8x⁴+2x³-7x²+3x-2 by 4x² - x + 1

2) First term of the quotient

  8x⁴ + 2x³ - 7x² + 3x - 2     | 4x² - x + 1
                                           ---------------------
 -8x⁴ + 2x³ - 2x²                   2x²
----------------------------------
           4x³ - 9x² + 3x - 2

3) Second term of the quotient:

  8x⁴ + 2x³ - 7x² + 3x - 2     | 4x² - x + 1
                                           ---------------------
 -8x⁴ + 2x³ - 2x²                   2x² + x
----------------------------------
           4x³ - 9x² + 3x - 2
          -4x³ +  x² -   x
        ----------------------------
                  - 8x² + 2x - 2

4) third term of the quotient:

  8x⁴ + 2x³ - 7x² + 3x - 2     | 4x² - x + 1
                                           ---------------------
 -8x⁴ + 2x³ - 2x²                   2x² + x - 2
----------------------------------
           4x³ - 9x² + 3x - 2
          -4x³ +  x² -   x
        ----------------------------
                  - 8x² + 2x - 2
                    8x²  - 2x + 2
                 -------------------------
                             0

5) Conclusion: since the remainder is 0, the division is exact and the quotient is 2x² + x - 2

You can verify the answer by multiplying the quotient obtained by the divisor. The result has to be the dividend.