End Behavior & Zeros of Polynomials

What is the relationship between the degree of a polynomial and the number of zeros?

• The degree of a polynomial indicates the maximum number of zeros it can have, counting multiplicities.

• The degree of a polynomial is always equal to the number of zeros it has.

• The degree of a polynomial has no relation to the number of zeros.

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

If a polynomial has a zero of multiplicity 3, what happens at that zero?

• It crosses the x-axis at that zero.

• It touches the x-axis and turns around.

• It does not intersect the x-axis.

• It approaches the x-axis but never touches it.

How do you determine the multiplicity of a zero?

• By finding the highest degree of the polynomial

• By evaluating the polynomial at that zero

• By the exponent of the factor associated with that zero in the polynomial's factored form

• By counting the number of times the zero appears in the polynomial

What is the end behavior of a polynomial function?

• It describes how the function behaves as x approaches positive or negative infinity, determined by the leading term of the polynomial.

• It indicates the maximum and minimum values of the function.

• It shows the points where the function intersects the x-axis.

• It represents the average rate of change of the function over its domain.

What are the zeros of the polynomial f(x) = (x - 2)(x - 3)(x + 1)?

• x = 2, x = 3, and x = -1

• x = 1, x = 2, and x = 3

• x = -2, x = -3, and x = 1

• x = 0, x = 2, and x = 3

How can you find the zeros of a polynomial function?

• By setting the polynomial equal to zero and solving for x.

• By factoring the polynomial into linear factors only.

• By taking the derivative of the polynomial and finding critical points.

• By evaluating the polynomial at various integer values.

What is the end behavior of a polynomial with an even degree and a positive leading coefficient?

• The ends of the graph rise in both directions.

• The ends of the graph fall in both directions.

• The graph rises on the left and falls on the right.

• The graph falls on the left and rises on the right.

What is the factored form of a polynomial?

• It expresses the polynomial as a sum of its coefficients.

• It expresses the polynomial as a product of its linear factors, which can reveal its zeros.

• It represents the polynomial in its standard form with all terms expanded.

• It shows the polynomial as a quotient of two polynomials.

What does it mean for a zero of a polynomial to 'cross' the x-axis?

• A zero crosses the x-axis if the polynomial changes sign at that zero, indicating an odd multiplicity.

• A zero crosses the x-axis if the polynomial remains constant at that zero, indicating an even multiplicity.

• A zero crosses the x-axis if the polynomial has no real roots at that point.

• A zero crosses the x-axis if the polynomial is always positive or always negative at that zero.

What does it mean for a zero of a polynomial to 'bounce' on the x-axis?

• A zero bounces on the x-axis if the polynomial does not change sign at that zero, indicating an even multiplicity.

• A zero bounces on the x-axis if the polynomial changes sign at that zero, indicating an odd multiplicity.

• A zero bounces on the x-axis if it is a complex number with a real part.

• A zero bounces on the x-axis if it is the only root of the polynomial.