Divide the equation?

Question

Divide 6m^3 - 4m^2n + 2n^3 by 2m - n and state the remainder as a single term

Answer 1

Rewrite the expression in long division form (6m³ - 4m²n + 2n³)/(2m - n).

Divide the first term of the dividend by the first term of the divisor 6m³/2m = 3m².

So,the first term of the quotient is 3m². Multiply (2m - n) by 3m² and subtract.

Divide the first term of the last row by first term of the divisor (- m²n)/2m = (- mn)/2.

So,the second term of the quotient is (- mn)/2. Multiply (2m - n) by (- mn)/2 and subtract.

Divide the first term of the last row by first term of the divisor  (- mn²/2)/2m = - n²/4.

So,the third term of the quotient is (- n²/4). Multiply (- n²/4) by (2m) and subtract.

Therefore, the remainder is 7n³/4.