Master finding all of the rational zeros of a polynomial without a calculator

The video tutorial explains how to find all zeros of a polynomial function without using technology. It covers the rational zero test and synthetic division as methods to identify rational zeros. The instructor demonstrates these techniques through example problems, emphasizing the importance of understanding these concepts for situations where calculators are not available.

Why is it important to understand how to find zeros without technology?

• To avoid using computers.

• To save time during exams.

• To be prepared for tests without calculators.

• Because technology is unreliable.

What is the purpose of the Rational Zero Test?

• To graph the polynomial.

• To find all complex zeros.

• To solve the polynomial equation.

• To identify potential rational zeros.

What does the Rational Zero Test involve?

• Listing all possible factors of the constant term.

• Using a calculator to find zeros.

• Graphing the polynomial.

• Solving the polynomial equation directly.

What is synthetic division used for in this context?

• To multiply polynomials.

• To graph the polynomial.

• To solve quadratic equations.

• To test potential zeros and find factors.

What is the first step in synthetic division?

• Add all coefficients together.

• Bring down the first coefficient.

• Multiply the polynomial by a factor.

• Divide the polynomial by a constant.

What should you do if synthetic division shows a remainder of zero?

• Ignore the result.

• Consider the divisor as a factor.

• Use a calculator to verify.

• Try a different divisor.

What is the next step after finding one factor using synthetic division?

• Stop the process.

• Use the quadratic formula.

• Factor the remaining polynomial.

• Graph the polynomial.

What is the benefit of factoring the remaining polynomial?

• It simplifies the polynomial.

• It confirms the graph of the polynomial.

• It eliminates complex numbers.

• It reveals all possible zeros.

What should you do if a polynomial cannot be factored easily?

• Use synthetic division again.

• Apply the quadratic formula.

• Graph the polynomial.

• Ignore the polynomial.

What is the final step in finding all zeros of a polynomial?

• List all solutions in a solution set.

• Graph the polynomial.

• Multiply all factors together.

• Divide the polynomial by its highest degree term.