Classifying, Adding/Subtracting, and Multiplying Polynomials

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

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial $$4x^3 + 2x^2 - x + 7$$ , the degree is 3.

A monomial is a polynomial with only one term. For example, $$5x^2$$ is a monomial.

A binomial is a polynomial with exactly two terms. For example, $$3x + 4$$ is a binomial.

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

To add polynomials, combine like terms. For example, to add $$(3x^2 + 2x) + (4x^2 - x)$$ , combine to get $$7x^2 + x$$ .

To subtract polynomials, distribute the negative sign and then combine like terms. For example, $$(5x^2 + 3) - (2x^2 + 1) = 3x^2 + 2$$ .

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in $$7x^5 - 9x^2 + 6x$$ , the leading coefficient is 7.

The area of a rectangle can be represented by the product of its length and width, which can be expressed as a polynomial. For example, if length = $$5x$$ and width = $$(5x - 4)$$ , then area = $$25x^2 - 20x$$ .

Like terms are terms that have the same variable raised to the same power. For example, $$3x^2$$ and $$5x^2$$ are like terms.