Exploring Polynomial Zeros and Multiplicities

What is a zero of a polynomial function?

• A zero of a polynomial function is a value that makes the polynomial equal to zero.

• A zero of a polynomial function is a constant term in the polynomial.

• A zero of a polynomial function is a value that makes the polynomial positive.

• A zero of a polynomial function is the highest degree term.

Which of the following is a zero of the polynomial f(x) = x^2 - 4?

• 3

• -1

• 2, -2

• 1

If a polynomial has a zero at x = 3 with multiplicity 2, what does this imply about the graph at x = 3?

• The graph is flat at x = 3.

• The graph crosses the x-axis at x = 3.

• The graph has a hole at x = 3.

• The graph touches the x-axis at x = 3 and does not cross it.

How many times does the zero x = -1 occur in the polynomial f(x) = (x + 1)^3(x - 2)?

• 4

• 2

• 1

• 3

What is the multiplicity of the zero x = 2 in the polynomial f(x) = (x - 2)^4?

• 4

• 5

• 3

• 2

Which of the following polynomials has a zero of multiplicity 1?

• (x - 2)

• (x + 3)

• (x^2 - 4)

• (x - 2)(x + 1)

What is the end behavior of the polynomial f(x) = -2x^3 + 5x - 1 as x approaches positive infinity?

• f(x) approaches positive infinity as x approaches positive infinity.

• f(x) approaches zero as x approaches positive infinity.

• f(x) approaches negative infinity as x approaches positive infinity.

• f(x) oscillates between positive and negative values as x approaches positive infinity.

How can you determine the multiplicity of a zero from the factored form of a polynomial?

• The multiplicity of a zero is the number of times it appears in the polynomial's standard form.

• The multiplicity of a zero is always equal to one for any polynomial.

• The multiplicity of a zero can be found by taking the derivative of the polynomial.

• The multiplicity of a zero is the exponent of its corresponding factor in the polynomial's factored form.

Which of the following is the correct factorization of the polynomial f(x) = x^2 - 5x + 6?

• (x - 4)(x - 2)

• (x + 2)(x + 3)

• (x - 1)(x - 6)

• (x - 2)(x - 3)

What is the end behavior of the polynomial f(x) = 3x^4 - 2x^2 + 1 as x approaches negative infinity?

• f(x) approaches a constant value as x approaches negative infinity.

• f(x) approaches negative infinity as x approaches negative infinity.

• f(x) approaches positive infinity as x approaches negative infinity.

• f(x) approaches zero as x approaches negative infinity.