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, combined using addition, subtraction, and multiplication.

Front

What is the leading coefficient of a polynomial?

Back

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

Front

What does it mean if a zero of a polynomial has multiplicity 2?

Back

It means that the zero is repeated twice, and the graph will 'bounce' off the x-axis at that zero.

Front

What is a constant term in a polynomial?

Back

The constant term is the term in a polynomial that does not contain any variables, representing the value of the polynomial when all variables are set to zero.

Front

How do you find the zeros of a polynomial?

Back

To find the zeros of a polynomial, set the polynomial equal to zero and solve for the variable.

Front

What is the significance of the x-intercepts of a polynomial graph?

Back

The x-intercepts of a polynomial graph are the points where the graph crosses or touches the x-axis, corresponding to the zeros of the polynomial.

Front

What is the end behavior of a polynomial function?

Back

The end behavior of a polynomial function describes how the function behaves as the input values approach positive or negative infinity, determined by the leading term.

Front

What is the difference between a polynomial and a rational function?

Back

A polynomial is a sum of terms with non-negative integer exponents, while a rational function is a ratio of two polynomials.

Front

What does it mean for a polynomial to be in standard form?

Back

A polynomial is in standard form when its terms are arranged in descending order of their degrees.