Given a Zero Determine the Remaining Zeros of a Polynomial

The video tutorial explains how to use synthetic division to find the zeros of a polynomial. It begins with an introduction to synthetic division and the importance of arranging terms in descending order. The instructor demonstrates the process step-by-step, highlighting key points such as handling missing terms and interpreting the results. The tutorial concludes with finding all zeros through factorization and applying the zero product property. Students are encouraged to apply these techniques to their homework problems.

What is the primary purpose of using synthetic division in polynomial equations?

• To calculate the integral of the polynomial

• To find the derivative of the polynomial

• To determine the degree of the polynomial

• To find the zeros of the polynomial

When setting up synthetic division, what must be ensured about the exponents of the polynomial?

• They should be in ascending order

• They should all be even numbers

• They should all be odd numbers

• They should be in descending order

In synthetic division, what do you do if a term is missing in the polynomial?

• Subtract one from the exponent of the next term

• Double the coefficient of the next term

• Add a zero coefficient for the missing term

• Ignore the missing term

After performing synthetic division, what is the next step to find all zeros of the polynomial?

• Differentiate the quotient polynomial

• Square the quotient polynomial

• Factor the quotient polynomial

• Integrate the quotient polynomial

What property is applied to solve for zeros after factoring the quotient polynomial?

• Distributive Property

• Associative Property

• Zero Product Property

• Commutative Property