The table represents the start of the division of 8x^4+2x^3-7x^2+3x-2 by the indicated divisor. Find the quotient.
2 answers:
Answer:
Answer: 2x² + x - 2 (the first option)
Step-by-step explanation:
got it right on quiz
Answer: <span><span>2x² + x - 2</span> (the first option)
Explanation:
1) Question: divide 8x⁴+2x³-7x²+3x-2 by 4x² - x + 1
2) First term of the quotient
</span><span> 8x⁴ + 2x³ - 7x² + 3x - 2 | 4x² - x + 1
---------------------
-8x⁴ + 2x³ - 2x² 2x²
----------------------------------
4x³ - 9x² + 3x - 2
3) Second term of the quotient:
</span>
<span> 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:
</span>
<span> 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 </span>2x² + x - 2
You can verify the answer by multiplying the quotient obtained by the divisor. The result has to be the dividend.
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