Divide the polynomial
f(x) = 3x²-x³-3x+5 by g(x) = x-1-x² and verify Division algorithm
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Answer: Let f(x) = 3x² - x³ - 3x + 5 and g(x) = x - 1 - x²
Long Division Method:
-x² + x - 1) -x³ + 3x² - 3x + 5(x - 2
-x³ + x² - x ------------------------
2x² - 2x + 5
2x² - 2x + 2
---------------------- 3 Verification:
Dividend = Divisor * Quotient + Remainder
= (-x² + x - 1) - (x - 2) + 3
= -x³ + x² - x + 2x² - 2x + 2 + 3
= 3x² - x³ - 3x + 5
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