# How can the Division Algorithm be used to check the quotient and remainder in a long division problem?

How can the Division Algorithm be used to check the quotient and remainder in a long division problem?
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Jane Acosta
The Division Algorithm can be used for checking the quotient in a long division problem by multiplying the divisor with the quotient. If the product is the same as the dividend, we have verified that the quotient is correct.
If the product of the quotient and divisor is not equal to the dividend, then the difference of the dividend and the product should be the remainder. If that condition is satisfied then we have verified that both the quotient and the remainder are correct solutions to the problem.
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tidones0r
Polynomial long division is an expanded variant of the well-known arithmetic technique of long division that divides a polynomial by another polynomial of the same or lower degree.
To check if the polynomial division is correct, multiply the divisor by the quotient, add the result to the remainder, and see if the dividend is obtained. Prefix a 0 as the coefficient to the word if the dividend does not contain a word adjacent to the greatest degree.