Question

Divide the polynomial
f(x) = 3x²-x³-3x+5 by g(x) = x-1-x² and verify Division algorithm​

Answer 1

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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