Dividing Polynomials

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, 2x^2 + 3x - 5 is a polynomial.

A monomial is a polynomial with only one term. For example, 5x^3 is a monomial.

Dividing a polynomial by a monomial involves dividing each term of the polynomial by the monomial.

Divide each term: (2x^8)/(2x) - (8x^2)/(2x) - (28x)/(2x) = x^7 - 4x - 14.

The result is 4.

Factor both the numerator and denominator, then cancel common factors to simplify.

The result is $$\frac{3x}{x + 4}$$ .

The result is $$\frac{3x + 5}{2x + 1}$$ .

The degree of a polynomial is the highest power of the variable in the polynomial.

Synthetic division is a simplified method of dividing a polynomial by a binomial of the form (x - c).