Multiplying and Dividing Polynomials

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

A monomial is a polynomial with only one term, such as 5x^2 or -3y.

A binomial is a polynomial with exactly two terms, such as 3x + 4 or x^2 - 5.

A trinomial is a polynomial with exactly three terms, such as x^2 + 3x + 2.

To multiply two monomials, multiply their coefficients and add their exponents for like bases. For example, (2x^3)(3x^2) = 6x^(3+2) = 6x^5.

The product of (a^m)(a^n) is a^(m+n).

The product of (3c)(10c) is 30c^2.

To multiply a monomial by a polynomial, distribute the monomial to each term of the polynomial. For example, 2x(3x + 4) = 6x^2 + 8x.

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

The leading coefficient is the coefficient of the term with the highest degree in a polynomial.