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Understanding Polynomial Concepts and Properties

Understanding Polynomial Concepts and Properties

Assessment

Interactive Video

•

Mathematics

•

9th - 10th Grade

•

Practice Problem

•

Hard

Created by

Thomas White

FREE Resource

The video tutorial explains the concept of rational roots, which are solutions to polynomial equations where the graph crosses the x-axis. It details the process of finding these roots by using the factors of the constant term and the leading coefficient. The tutorial demonstrates how to test potential rational roots using synthetic division and shows how to factor polynomials to find all zeros. Finally, it provides guidance on sketching the graph of the polynomial based on its roots and end behavior.

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27 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does the term 'rational root' refer to in the context of equations?

A root that is always positive

A root that is a fraction

A root that is a solution to the equation

A root that is an integer

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in finding rational roots of a polynomial?

Using the quadratic formula

Finding the derivative of the polynomial

Listing all possible factors of the constant term

Graphing the polynomial

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How do you determine the possible rational roots of a polynomial?

By multiplying the factors of the constant and leading coefficient

By subtracting the factors of the leading coefficient from the constant

By adding the factors of the constant and leading coefficient

By dividing the factors of the constant by the factors of the leading coefficient

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does it mean if a polynomial is not easily factored?

It has no roots

It is a linear polynomial

It is a quadratic polynomial

It may require the use of the rational root theorem

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does it mean if a polynomial is cubic?

It has three roots

It has a degree of three

It has three x-intercepts

It has three terms

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the purpose of the rational root theorem?

To find the derivative of a polynomial

To find the roots of a polynomial

To find the maximum point of a polynomial

To find the y-intercepts of a polynomial

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of dividing the factors of the constant by the factors of the leading coefficient?

The derivative of the polynomial

The y-intercepts of the polynomial

The possible rational roots

The maximum point of the polynomial

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