Graphing Polynomials

What is multiplicity in relation to polynomial zeros?

• Multiplicity refers to the number of times a particular zero appears in a polynomial.

• Multiplicity is the degree of the polynomial.

• Multiplicity indicates the highest power of the variable in the polynomial.

• Multiplicity is the sum of all the coefficients in the polynomial.

What is a zero of a polynomial?

• A value of x that makes the polynomial equal to one.

• A value of x that makes the polynomial equal to zero.

• A value of x that is always positive.

• A value of x that is the highest degree of the polynomial.

What is the significance of the leading coefficient in a polynomial?

• It determines the number of roots the polynomial has.

• It affects the end behavior of the polynomial's graph.

• It is the constant term of the polynomial.

• It indicates the polynomial's degree.

What does it mean for a polynomial to be factored completely?

• A polynomial is factored completely when it is expressed as a product of irreducible polynomials over the real numbers.

• A polynomial is factored completely when it has no real roots.

• A polynomial is factored completely when it is expressed as a sum of its coefficients.

• A polynomial is factored completely when it can be divided by any integer.

What is a polynomial?

• A mathematical expression with variables raised to a (non-negative) integer power or degree.

• A type of equation that includes only constants and no variables.

• A mathematical expression that can only include positive integers.

• A function that has a variable raised to a negative power.

How do you determine if a polynomial is odd or even?

• A polynomial is even if all its terms have even degrees.

• A polynomial is odd if it has both even and odd degree terms.

• A polynomial is even if it has both even and odd degree terms.

• A polynomial is odd if all its terms have even degrees.

How do you find the zeros of a polynomial?

• Set the polynomial equal to zero and solve for x.

• Add the coefficients of the polynomial together.

• Multiply the polynomial by a constant.

• Graph the polynomial and find the x-intercepts.

What is the Fundamental Theorem of Algebra?

• Every polynomial function has at least one real root.

• Every non-constant polynomial function has at least one complex root.

• All polynomial functions can be factored into linear factors over the reals.

• The degree of a polynomial function determines the number of its roots.

What does the end behavior of a polynomial describe?

• How the polynomial behaves as the input approaches positive or negative infinity.

• The maximum and minimum values of the polynomial.

• The number of roots the polynomial has.

• The symmetry of the polynomial graph.

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

• A polynomial of degree n can have up to n real zeros, counting multiplicities.

• A polynomial of degree n can have exactly n real zeros, with no exceptions.

• A polynomial of degree n can have at least n real zeros, but no more than n+1.

• A polynomial of degree n can have no more than n-1 real zeros.