Adding and Subtracting 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, $$4x^3$$ is a monomial.

A binomial is a polynomial with exactly two terms. For example, $$3x + 5$$ is a binomial.

A trinomial is a polynomial with exactly three terms. For example, $$x^2 + 2x + 1$$ is a trinomial.

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in $$-2x^5 + 3x$$ , the degree is 5.

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in $$-2x^5 + 3x$$ , the leading coefficient is -2.

To add polynomials, combine like terms. For example, $$(2x^2 + 3x) + (4x^2 + 5) = (2x^2 + 4x^2) + 3x + 5 = 6x^2 + 3x + 5$$ .

To subtract polynomials, distribute the negative sign and then combine like terms. For example, $$(3x^2 + 2x) - (x^2 + 4) = (3x^2 - x^2) + 2x - 4 = 2x^2 + 2x - 4$$ .

A quintic polynomial is a polynomial of degree 5. For example, $$x^5 - 3x^4 + 2x^3 - x + 1$$ is a quintic polynomial.

A quartic polynomial is a polynomial of degree 4. For example, $$2x^4 + 3x^3 - x + 7$$ is a quartic polynomial.