Finding Zeros of Polynomial Functions

The video tutorial explains how to find the zeros or roots of a polynomial function. It presents two methods: graphing the function to identify real rational zeros and using the Rational Roots Theorem. The tutorial demonstrates using a graph to find zeros, focusing on a cubic function with three real zeros. It explains factoring the polynomial using synthetic division and solving the quadratic factor to find all zeros. The video concludes by summarizing the process and verifying the zeros found.

What are the two methods mentioned for finding the zeros of a polynomial function?

• Graphing and Rational Roots Theorem

• Synthetic Division and Factoring

• Long Division and Rational Roots Theorem

• Quadratic Formula and Graphing

What does the graph of a cubic function with three x-intercepts indicate?

• Three real zeros

• Two real zeros and one complex zero

• One real zero and two complex zeros

• No real zeros

Which zero is used to help factor the given polynomial function?

• x = 1/2

• x = 0

• x = -5/3

• x = +3

What method is used to find the quadratic factor of the polynomial?

• Completing the Square

• Factoring by Grouping

• Synthetic Division

• Long Division

What are the coefficients used in synthetic division for the polynomial?

• 2, -1, 6, -3

• 3, 5, -7, 1

• 1, -3, 2, -5

• 6, -11, -26, 15

What is the quadratic factor obtained after synthetic division?

• 3x^2 + 5x - 1

• 6x^2 + 7x - 5

• x^2 - 4x + 4

• 2x^2 + 3x - 5

Which method is suggested if the quadratic factor is not easily factorable?

• Quadratic Formula

• Synthetic Division

• Rational Roots Theorem

• Graphing

What are the remaining zeros found after factoring the quadratic?

• x = 0 and x = 3

• x = 1 and x = -2

• x = 2 and x = -1

• x = -5/3 and x = 1/2

How can the zeros be verified according to the video?

• By using the Rational Roots Theorem

• By checking the graph

• By performing long division

• By using the quadratic formula

What is the significance of the zeros being real and rational?

• They cannot be found using the Rational Roots Theorem

• They are imaginary numbers

• They can be found using the graph

• They are complex numbers