How can the division algorithm be used to check the result of the polynomial division.

The division algorithm is generally represented as,
Dividend = (Divisor) Quotient) + Remainder
Where the degree of the divisor is less than or equal to the degree of dividend and there must exist unique polynomial quotient and the remainder in which the degree of the remainder is less than the divisor or the remainder is the zero of the polynomials.
After performing the division, the result must be represented in the form of (Divisor) (Quotient) + Remainder and then the expression is simplified which must be equal to the dividend.
Therefore, the division algorithm is generally represented as $f(x)=d(x)q(x)+r(x)$.