Question 2.4.3: Long Division of Polynomials Divide 6x^4 + 5x³ + 3x - 5 by 3...

We write the dividend, 6 x^4+5 x^3+3 x-5, as 6 x^4+5 x^3+0 x^2+3 x-5 to keep all like terms aligned.

The division process is finished because the degree of 7x – 5, which is 1, is less than the degree of the divisor 3x² – 2x, which is 2. The answer is

\frac{6 x^4+5 x^3+3 x-5}{3 x^2-2 x}=2 x^2+3 x+2+\frac{7 x-5}{3 x^2-2 x}.