Full Class Zeros and multiplicity of a polynomial

The video tutorial covers polynomial equations, focusing on solutions, zeros, and the zero product property. It explains how to solve polynomial equations by factoring and discusses the relationship between zeros and solutions. The concept of multiplicity is introduced, explaining how it affects graph behavior. The tutorial concludes with instructions for a group activity to reinforce the concepts learned.

What is a zero of a polynomial function?

• A point where the graph touches the y-axis

• A solution to the equation F(x) = 0

• A factor of the polynomial

• A point where the graph crosses the y-axis

Why is factoring a polynomial important when solving equations?

• It changes the polynomial into a linear equation

• It eliminates the need for graphing

• It simplifies the polynomial to a single term

• It allows us to apply the Zero Product Property

According to the Zero Product Property, if a*b = 0, what must be true?

• Both a and b must be zero

• Neither a nor b can be zero

• a and b must be equal

• Either a or b must be zero

How are solutions and zeros related in a polynomial equation?

• Solutions are the roots, while zeros are the exponents

• Zeros are the factors, while solutions are the coefficients

• Solutions and zeros are the same and make the equation true

• Solutions are the x-intercepts, while zeros are the y-intercepts

What is the factored form of a polynomial if one of its zeros is 3?

• X * 3

• X + 3

• 3X

• X - 3

What does the exponent in a polynomial expression indicate?

• The number of times the base is multiplied by itself

• The number of terms in the polynomial

• The degree of the polynomial

• The coefficient of the leading term

What is the multiplicity of a zero in a polynomial?

• The number of times the zero appears as a solution

• The degree of the polynomial

• The sum of all zeros

• The product of all factors

If a polynomial graph touches the x-axis at a point, what can be inferred about the zero's multiplicity?

• The multiplicity is even

• The zero is a complex number

• The multiplicity is odd

• The zero is not a real number

What happens to the graph of a polynomial at an x-intercept if the zero's multiplicity is odd?

• The graph touches the x-axis

• The graph crosses the x-axis

• The graph remains below the x-axis

• The graph remains above the x-axis

How does the multiplicity of a zero affect the graph of a polynomial?

• It alters the leading coefficient

• It changes the degree of the polynomial

• It affects whether the graph touches or crosses the x-axis

• It determines the number of x-intercepts