Polynomial Zeros

Front

What is a polynomial zero?

Back

A polynomial zero is a value of x that makes the polynomial equal to zero. It is also known as a root of the polynomial.

Front

How do you find the zeros of a polynomial function?

Back

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

Front

What is the significance of the y-intercept in a polynomial function?

Back

The y-intercept is the point where the graph of the polynomial crosses the y-axis, found by evaluating the function at x=0.

Front

What does the degree of a polynomial indicate about its zeros?

Back

The degree of a polynomial indicates the maximum number of zeros it can have.

Front

What is the end behavior of a polynomial function?

Back

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

Front

What is the relationship between the coefficients and the zeros of a polynomial?

Back

The coefficients of a polynomial can affect the location and multiplicity of its zeros.

Front

What does it mean for zeros to come in pairs?

Back

Zeros that involve square roots or complex numbers often appear in conjugate pairs due to the Fundamental Theorem of Algebra.

Front

How do you determine the multiplicity of a zero?

Back

The multiplicity of a zero is determined by the exponent of the factor in the polynomial that corresponds to that zero.

Front

What is the Factor Theorem?

Back

The Factor Theorem states that if f(c) = 0 for a polynomial f(x), then (x - c) is a factor of f(x).

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that the remainder of the division of a polynomial f(x) by (x - c) is equal to f(c).