Basics of Polynomial Division

Polynomial division is a process where we have two polynomials: the dividend (the polynomial we are dividing) and the divisor (the polynomial we divide by). The result is the quotient, which is also a polynomial, and in some cases we also get a remainder.

The Division Procedure

Arrange the polynomials First, we write both polynomials in descending powers of the variable.
Divide the leading terms We divide the leading term of the dividend by the leading term of the divisor. The result becomes the next term of the quotient.
Multiply and subtract We multiply the divisor by this term of the quotient and subtract that product from the current dividend. What is left becomes the new dividend.
Repeat the process We repeat the same steps with the new dividend. We continue until the degree of the new dividend is lower than the degree of the divisor.
Remainder If the degree of the current dividend becomes smaller than the degree of the divisor and we cannot continue dividing, the remaining polynomial is the remainder.