Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to whole number powers and coefficients, combined using addition, subtraction, and multiplication.

Front

What are the zeros of a polynomial?

Back

The zeros of a polynomial are the values of the variable that make the polynomial equal 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 degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.

Front

What is a leading coefficient?

Back

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

Front

What does it mean if a polynomial has a negative leading coefficient?

Back

If a polynomial has a negative leading coefficient, the graph of the polynomial will fall to the right as x approaches positive infinity.

Front

What is multiplicity in relation to polynomial zeros?

Back

Multiplicity refers to the number of times a particular zero is repeated in a polynomial.

Front

What effect does an even multiplicity have on the graph of a polynomial at its x-intercept?

Back

An even multiplicity means the graph will 'bounce off' the x-axis at that intercept.

Front

What effect does an odd multiplicity have on the graph of a polynomial at its x-intercept?

Back

An odd multiplicity means the graph will 'cross through' the x-axis at that intercept.

Front

How do you write a polynomial given its zeros?

Back

To write a polynomial given its zeros, use the factored form: (x - zero1)(x - zero2)...(x - zeroN).