Divide 3x2 - x3 - 3x + 5 by x - 1 - x2 and verify the division algorithm.

Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM

Expert Answer:

Let f(x) = -x3 + 3x2 - 3x + 5 and g(x) = -x2 + x - 1

We have:

Quotient, q(x) = x - 2 and remainder, r(x) = 3

Now,

Quotient Divisor + Remainder

= (x - 2)(-x2 + x - 1) + 3

= -x3 + x2 - x + 2x2 - 2x + 2 + 3

= -x3 + 3x2 - 3x + 5 = Dividend

Hence, the division algorithm is verified.

Answered by  | 4th Jun, 2014, 03:23: PM

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