Question

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 1

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

Step-by-step explanation:

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Answer 2

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

Step-by-step 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.