Classifying Polynomials Flashcard

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 quadratic polynomial is a polynomial of degree 2, which can be expressed in the form $$ax^2 + bx + c$$ where a, b, and c are constants and a ≠ 0. Example: $$x^2 - 6x + 9$$ .

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in $$5x^5 - 4x^3 + 3x - 2$$ , the leading coefficient is 5.

The degree of a polynomial is the highest power of the variable in the polynomial. For example, the degree of $$4x^3 - 5x^2 + 7$$ is 3.

The degree of the polynomial is 5.

The degree of the polynomial is 1.

A monomial is a polynomial with only one term. For example, $$3x^2$$ is a monomial.

A binomial is a polynomial with exactly two terms. For example, $$x^2 - 4$$ is a binomial.

A trinomial is a polynomial with exactly three terms. For example, $$x^2 + 5x + 6$$ is a trinomial.

The standard form of a polynomial is when the terms are arranged in descending order of their degrees. For example, $$3x^4 + 2x^3 - x + 5$$ .