The video tutorial explains how to find rational zeros of a polynomial function. It begins with an introduction to the concept and the importance of understanding zeros beyond using technology. The rational zero test is explained, followed by a discussion on factoring techniques and their limitations. The tutorial then demonstrates using synthetic division and the remainder theorem to verify potential zeros. Finally, graphing is used to visualize the function, and the process is concluded with a summary of the findings.

Why is it important to learn how to find rational zeros manually?

• Because it's faster than using technology.

• To understand the underlying mathematical concepts.

• To avoid using calculators.

• Because technology is unreliable.

What does the Rational Zero Test help determine?

• The complex zeros of a polynomial.

• The exact zeros of a polynomial.

• All possible rational zeros of a polynomial.

• The irrational zeros of a polynomial.

In the Rational Zero Test, what does 'P' represent?

• The degree of the polynomial.

• The factors of the constant term.

• The factors of the leading coefficient.

• The sum of the coefficients.

What is a key step in verifying potential zeros without technology?

• Using the quadratic formula.

• Graphing the polynomial.

• Applying synthetic division.

• Using a calculator.

What is the purpose of synthetic division in this context?

• To simplify the polynomial.

• To find the derivative of the polynomial.

• To verify if a number is a zero of the polynomial.

• To find the degree of the polynomial.

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

• A remainder of zero.

• A positive remainder.

• A remainder equal to the leading coefficient.

• A negative remainder.

What are the zeros of the polynomial after applying synthetic division?

• 3, -2, and 1

• 6, -5, and 0

• 5, -4, and 2

• 4, -1, and -3