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.
