What is the quotient when 2m^2-m+3 is divided by (2-m) leaving a remainder 9

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Solution

When you are dividing 2m^2-m+3 by (2-m) and there is a remainder of 9, it means that the 9 is in excess. So deduct 9 from the dividend to make it 2m^2-m-6. Then the divisor (2-m) will give you the quotient of -2m-3.

Check: (2-m)(-2m-3) = 2m^2-m-6.

2m^2-m+3 - [2m^2-m-6] = 9. Correct.

The quotient is -(2m+3).

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