What is the process of polynomial division?

Polynomial division is the process of dividing one polynomial by another polynomial.

Polynomial division is a method used to divide one polynomial by another polynomial. The process is similar to long division, but instead of dividing numbers, we divide polynomials. The goal is to find the quotient and remainder of the division.

To perform polynomial division, we first write the dividend (the polynomial being divided) and the divisor (the polynomial we are dividing by) in descending order of degree. We then divide the first term of the dividend by the first term of the divisor to get the first term of the quotient. We then multiply the entire divisor by this term and subtract it from the dividend. This gives us a new polynomial, which we then repeat the process with until we have no more terms left to divide.

For example, let's divide x^3 + 2x^2 - 3x - 4 by x - 2. We start by writing the dividend and divisor in descending order of degree:

x^3 + 2x^2 - 3x - 4 ÷ x - 2

We then divide the first term of the dividend by the first term of the divisor:

x^3 ÷ x = x

This gives us the first term of the quotient. We then multiply the entire divisor by this term:

(x - 2) x = x^2 - 2x

We subtract this from the dividend:

x^3 + 2x^2 - 3x - 4 - (x^2 - 2x) = x^3 + x^2 - x - 4

We then repeat the process with this new polynomial:

x^3 + x^2 - x - 4 ÷ x - 2

x^3 ÷ x = x

(x - 2) x = x^2 - 2x

x^3 + x^2 - x - 4 - (x^2 - 2x) = x^3 - x^2 + 3x - 4

x^3 - x^2 + 3x - 4 ÷ x - 2

x^3 ÷ x = x

(x - 2) x = x^2 - 2x

x^3 - x^2 + 3x - 4 - (x^2 - 2x) = x^3 -