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Answer :
Final answer:
To divide the given polynomials, we can use polynomial long division. The final quotient is 5x² - 15x + 1, and the remainder is -50x³ + 24x⁴ + 5x.
Explanation:
To divide the expression (5x + 35 + 24x⁴ + 20x⁵ - x² - 33x³ + 5x⁶) by the expression (x² - 10x + 3x³ + 9 + x⁴), we can use polynomial long division.
Divide the highest degree terms: (5x⁶) ÷ (x⁴) = 5x².
Multiply the divisor by the quotient obtained: (x² - 10x + 3x³ + 9 + x⁴) x (5x²) = 5x⁴ - 50x³ + 15x⁵ + 45x² + 5x⁶.
Subtract this new polynomial from the original polynomial (5x + 35 + 24x⁴ + 20x⁵ - x² - 33x³ + 5x⁶): (5x + 35 + 24x⁴ + 20x⁵ - x² - 33x³ + 5x⁶) - (5x⁴ - 50x³ + 15x⁵ + 45x² + 5x⁶) = -50x³ + 24x⁴ + 5x.
Repeat the process with the new polynomial as the dividend and continue until there are no more terms remaining to divide. The final quotient is 5x² - 15x + 1, and the remainder is -50x³ + 24x⁴ + 5x.
Learn more about Polynomial long division here:
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