Learn How to Synthetically Divide Twice to Find All the Zeros of the Polynomial

The video tutorial covers the rational zero test, explaining how it identifies possible rational zeros of a polynomial. It highlights the importance of graphing and common mistakes in synthetic division, such as missing place values. The tutorial demonstrates the synthetic division process, showing how to find factors and zeros, including imaginary solutions. The video emphasizes understanding the difference between real and imaginary zeros and how to apply these concepts to solve polynomial equations.

What does the rational zero test help determine?

• The exact zeros of a polynomial

• Possible rational zeros of a polynomial

• The degree of a polynomial

• The imaginary zeros of a polynomial

Why is it important to consider imaginary numbers when finding zeros?

• They are always real numbers

• They can be part of the solution set

• They are not part of the solution set

• They simplify the polynomial

What common mistake do students make in synthetic division?

• Ignoring the constant term

• Forgetting to include all terms

• Using the wrong divisor

• Not factoring the polynomial

What should you do if a term is missing in a polynomial during synthetic division?

• Skip the division process

• Ignore the missing term

• Add a random number

• Use zero as a placeholder

How can you find all zeros of a polynomial?

• Only by using a calculator

• By guessing

• Using synthetic division and graphing

• Only by factoring

What is the result of taking the square root of a negative number in the real number system?

• A real number

• An imaginary number

• A rational number

• An irrational number

Which of the following is not a type of zero that can be found in a polynomial?

• Complex zero

• Fractional zero

• Imaginary zero

• Rational zero