Using Rational Zero Test and All Zeros of a Polynomial

The video tutorial covers the process of finding zeros of a polynomial, focusing on the rational zero test and synthetic division. It explains how to identify possible rational zeros using the factors of P/Q and demonstrates methods to test these zeros without a graphing calculator. The tutorial also includes a step-by-step verification of rational zeros and concludes with a summary and Q&A session.

What is the primary purpose of finding zeros in a polynomial?

• To find the polynomial's maximum value

• To perform synthetic division

• To simplify the polynomial

• To determine the degree of the polynomial

Which of the following is a step in the Rational Zero Test?

• Calculating the polynomial's integral

• Graphing the polynomial

• Using the factors of the constant term and leading coefficient

• Finding the derivative of the polynomial

What does the Factor and Remainder Theorem help determine?

• The polynomial's symmetry

• The maximum value of the polynomial

• If a number is a zero of the polynomial

• The degree of the polynomial

What is the result of synthetic division if a number is a zero of the polynomial?

• A non-zero remainder

• A zero remainder

• A negative remainder

• A positive remainder

Which number was confirmed as a rational zero in the example?

• 1

• -3

• -1

• 3

What is the factor of the polynomial if -3 is a zero?

• X - 1

• X + 3

• X - 3

• X + 1

What additional zeros are found after factoring the polynomial?

• ± sqrt 2

• ± sqrt 3

• ± sqrt 5

• ± sqrt 7