Understanding Real Zeros of Polynomial Functions

This video tutorial explains how to determine the real zeros of a polynomial using a graphing calculator. It begins with a review of real zeros and polynomial functions, then demonstrates how to find real zeros by identifying x-intercepts on a graph. The tutorial also covers rewriting functions in factored form and understanding the concept of multiplicity. Finally, it addresses complex zeros and uses synthetic division to find them, providing a comprehensive guide to analyzing polynomial functions graphically and algebraically.

What is a real zero of a function?

• A value of x where the function is undefined

• A value of x where the function has a maximum

• A value of x where the function has a minimum

• A value of x where the function equals zero

What do x-intercepts of a polynomial function represent?

• The points where the graph has a minimum

• The points where the graph touches the y-axis

• The points where the graph crosses the x-axis

• The points where the graph has a maximum

How can you find the real zeros of a polynomial using a graphing calculator?

• By using the derivative function

• By using the zero or root feature

• By using the integral function

• By using the maximum feature

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

• If x = a is a zero, then x + a is a factor

• If x = a is a zero, then x - a is a factor

• Zeros are the same as factors

• Zeros are the opposite of factors

How can the T-table be used in finding zeros?

• By checking where the function value is maximum

• By checking where the function value is undefined

• By checking where the function value is minimum

• By checking where the function value is zero

What does it mean if a zero has multiplicity 2?

• The zero is not counted

• The zero is a maximum point

• The zero is counted twice

• The zero is a complex number

How can you rewrite a polynomial in factored form using its zeros?

• By multiplying the zeros

• By using the zeros to form factors

• By subtracting the zeros

• By adding the zeros

What is the purpose of synthetic division in finding zeros?

• To find the maximum value of the function

• To find the minimum value of the function

• To integrate the polynomial

• To divide the polynomial and find complex zeros

What are complex zeros?

• Zeros that are real numbers

• Zeros that are imaginary numbers

• Zeros that are undefined

• Zeros that are maximum points

How do you find the complex zeros of a polynomial?

• By finding the derivative of the polynomial

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

• By finding the integral of the polynomial

• By setting the polynomial equal to one and solving for x