Find All of the Zeros of a Polynomial Without Graphing

The video tutorial explains how to find all zeros of a polynomial using the Rational Zeros Theorem and synthetic division. It begins with identifying possible rational zeros, then applies synthetic division to test these zeros. The polynomial is further factored to find additional zeros, and the process concludes with solving the factored polynomial to identify all zeros. The tutorial emphasizes understanding the steps and using tools like graphing calculators to verify results.

What is the first step in finding the zeros of a polynomial?

• Finding the derivative

• Using the quadratic formula

• Graphing the polynomial

• Listing all possible rational zeros

Which of the following is a potential rational zero for the polynomial 2x^3 + 7x^2 - 7x - 12?

• 3

• 1

• 5

• 0

What method is used to verify if a number is a zero of a polynomial?

• Substitution

• Long division

• Graphical method

• Synthetic division

After finding one zero, what is the next step in solving the polynomial?

• Graph the polynomial

• Differentiate the polynomial

• Use the quadratic formula

• Factor the polynomial

Which of the following pairs of numbers multiply to -24 and add to 5?

• 6 and -4

• 8 and -3

• 5 and -5

• 7 and -2

What is the zero of the polynomial 2x^2 + 5x - 12 after factoring?

• -1

• -4

• 2

• 3/2

Which of the following is a rational zero of the polynomial 2x^3 + 7x^2 - 7x - 12?

• 0

• -1

• 2

• 1