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 how to use synthetic division to factor the polynomial and find remaining zeros. The video concludes by verifying the zeros and discussing the potential use of the quadratic formula if factoring is challenging.

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

• Graphing and using the Rational Roots Theorem

• Using the Quadratic Formula and completing the square

• Graphing and using synthetic division

• Using the Rational Roots Theorem and factoring

Tags

CCSS.HSF-IF.C.7C

What does the Rational Roots Theorem help us determine?

• The degree of the polynomial

• The possible rational zeros

• The constant term

• The leading coefficient

Tags

CCSS.HSA.APR.B.2

How many real zeros does a cubic function have?

• One

• Two

• Three

• Four

Tags

CCSS.HSF-IF.C.7C

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

• x = -5/3

• x = 1/2

• x = 3

• x = -1

Tags

CCSS.HSF-IF.C.7C

What method is used to factor the polynomial after identifying the zero at x = 3?

• Completing the square

• Long division

• Quadratic formula

• Synthetic division

Tags

CCSS.HSA.APR.D.6

What are the coefficients of the quadratic factor obtained after synthetic division?

• 6, -11, -26, 15

• 6, 7, -5

• 3, 2, -5

• 1, -3, 2

Tags

CCSS.HSA.APR.D.6

Which method is used to solve the quadratic factor for its zeros?

• Graphing

• Synthetic division

• Quadratic formula

• Factoring

Tags

CCSS.HSA-REI.B.4B

What are the remaining two zeros of the polynomial after factoring the quadratic?

• x = 2/3 and x = -1/2

• x = 1 and x = -2

• x = -5/3 and x = 1/2

• x = 3 and x = -1

Tags

CCSS.HSF-IF.C.7C

What is the sum of the inner and outer products when factoring the quadratic 6x^2 + 7x - 5?

• 5x

• 3x

• 10x

• 7x

How can the zeros of the polynomial be verified?

• By using the Rational Roots Theorem

• By graphing the polynomial

• By using synthetic division

• By using the quadratic formula

Tags

CCSS.HSF-IF.C.7C