Understanding Polynomial Functions and Zeros

The video tutorial explains how to find an equation of a polynomial function with real coefficients given specific zeros. It covers the significance of zeros in determining polynomial factors, methods to clear fractions from factors, and the process of deriving and simplifying the polynomial function. The tutorial concludes with a graphical verification of the polynomial zeros.

What information do the zeros of a polynomial function provide?

• The constant term

• The leading coefficient

• The factors of the polynomial

• The degree of the polynomial

Why is a constant introduced when dealing with fractional zeros?

• To eliminate fractions in the polynomial coefficients

• To change the zeros of the polynomial

• To simplify the polynomial to a linear function

• To increase the degree of the polynomial

What happens to the polynomial function when a constant is multiplied with the factors?

• The fractions are cleared

• The polynomial becomes linear

• The degree increases

• The zeros change

How can you convert a zero of -2/3 into a factor without fractions?

• Multiply by 3 and add 2

• Subtract 2 from both sides

• Add 3 to both sides

• Multiply by 2

Which of the following is a factor of the polynomial if the zero is 3/7?

• X - 3/7

• 3X + 7

• 7X + 3

• 7X - 3

What is the first step in multiplying the factors to form the polynomial function?

• Add all the factors together

• Multiply the first two binomials

• Divide the factors by a constant

• Subtract the factors from each other

What is the result of multiplying 3X by 7X in the polynomial?

• 21X

• 21X squared

• 10X squared

• 10X

What is the final form of the polynomial function after combining like terms?

• 21X cubed + 5X - 6

• 21X cubed + 5X squared - 6

• 21X squared + 26X - 6

• 21X cubed + 26X squared - X - 6

How do you verify the zeros of a polynomial function graphically?

• By checking the y-intercepts

• By calculating the area under the curve

• By identifying the x-intercepts

• By finding the slope of the graph

What is the significance of the x-intercepts in the graph of a polynomial function?

• They are the points where the graph is undefined

• They show the minimum points

• They indicate the zeros of the function

• They represent the maximum points