Note that we stop the division process when either the remainder is zero or its degree is less than the degree of the divisor. So, here the quotient is 2x – 1 and the remainder is 3. Also,
(2x – 1)(x + 2) + 3 = 2x2 + 3x – 2 + 3 = 2x2 + 3x + 1
i.e., 2x2 + 3x + 1 = (x + 2)(2x – 1) + 3
Therefore, Dividend = Divisor × Quotient + Remainder
Let us now extend this process to divide a polynomial by a quadratic polynomial.