Polynomial Graphs

Front

What is a polynomial?

Back

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

Front

What is the degree of a polynomial?

Back

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

Front

What is a leading coefficient?

Back

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

Front

What is the end behavior of a polynomial?

Back

The end behavior of a polynomial describes how the values of the polynomial behave as x approaches positive or negative infinity.

Front

What is a quadratic polynomial?

Back

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.

Front

What is a cubic polynomial?

Back

A cubic polynomial is a polynomial of degree 3, which can be expressed in the form ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and a ≠ 0.

Front

What is a quartic polynomial?

Back

A quartic polynomial is a polynomial of degree 4, which can be expressed in the form ax^4 + bx^3 + cx^2 + dx + e, where a, b, c, d, and e are constants and a ≠ 0.

Front

What is a quintic polynomial?

Back

A quintic polynomial is a polynomial of degree 5, which can be expressed in the form ax^5 + bx^4 + cx^3 + dx^2 + ex + f, where a, b, c, d, e, and f are constants and a ≠ 0.

Front

How do you find the roots of a polynomial?

Back

The roots of a polynomial are the values of x that make the polynomial equal to zero. They can be found using factoring, the quadratic formula, or numerical methods.

Front

What is the difference between even and odd degree polynomials?

Back

Even degree polynomials have the same end behavior on both sides (both up or both down), while odd degree polynomials have opposite end behavior (one side up and the other side down).