Dividing Polynomials by monomials

A monomial is a polynomial with only one term, which can be a constant, a variable, or a product of constants and variables raised to non-negative integer powers.

Dividing a polynomial by a monomial involves simplifying each term of the polynomial by the monomial, reducing the degree of the terms.

$$5x^6$$ .

5x^8.

$$4x^2 + 2x - 1$$ .

Identify the leading term of the polynomial and divide it by the monomial.

$$4x - 2 + \frac{6}{x}$$ .

$$3x + 2$$ .

For a polynomial P(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0 and a monomial m = bx^k, the result is P(x)/m = (a_n/b)x^{n-k} + (a_{n-1}/b)x^{n-1-k} + ... + (a_1/b)x^{1-k} + (a_0/b)x^{-k}.

The degree of the term decreases by the degree of the monomial.