Question 2.4.2: Long Division of Polynomials Divide 4 - 5x - x² + 6x³ by 3x ...

We begin by writing the dividend in descending powers of x.

4 – 5x – x² + 6x³ = 6x³ – x² – 5x + 4

Now we divide 3x² by 3x to obtain x, multiply x and the divisor, and subtract.

Now we divide –3x by 3x to obtain –1, multiply –1 and the divisor, and subtract.

The quotient is 2x² + x – 1 and the remainder is 2. When there is a nonzero remainder, as in this example, list the quotient, plus the remainder above the divisor. Thus,