Note that the given polynomials are not in standard form. To carry out division, we first write both the dividend and divisor in decreasing orders of their degrees.
So, dividend = –x3 + 3x2 – 3x + 5 and divisor = –x2 + x – 1.
Division process is shown on the right side.
We stop here since degree (3) = 0 < 2 = degree (–x2 + x – 1).
So, quotient = x – 2, remainder = 3.
Now,
Divisor × Quotient + Remainder
= (–x2 + x – 1) (x – 2) + 3
= –x3 + x2 – x + 2x2 – 2x + 2 + 3
= –x3 + 3x2 – 3x + 5
= Dividend
In this way, the division algorithm is verified.
