Polynomial Zeros and Synthetic Division

The video tutorial explains how to graph a polynomial that cannot be factored using regular rules. It introduces the rational zeros theorem to list possible zeros and uses synthetic division to find actual zeros. The polynomial is then factored, and zeros are identified along with their multiplicity. Finally, the polynomial is graphed, considering end behavior and plotting additional points for accuracy.

What is the main challenge with the polynomial in this example?

• It is already factored.

• It cannot be factored using regular rules.

• It has no real zeros.

• It is a linear polynomial.

Why won't factoring by grouping work for this polynomial?

• It has too many terms.

• The terms do not group into factors.

• It is already in simplest form.

• The polynomial is quadratic.

What theorem is used to list possible zeros of the polynomial?

• Fundamental Theorem of Algebra

• Rational Zeros Theorem

• Binomial Theorem

• Intermediate Value Theorem

What is the first step in using the rational zeros theorem?

• Identify the leading coefficient.

• List the factors of the constant term.

• Graph the polynomial.

• Find the degree of the polynomial.

What is the constant term of the polynomial?

• 2

• 1

• 3

• 6

What is the result of dividing 6 by 2 in the context of the rational zeros theorem?

• 1

• 2

• 3

• 4

What is the goal of synthetic division in this context?

• To simplify the polynomial.

• To find the degree of the polynomial.

• To determine the leading coefficient.

• To find zeros with a remainder of zero.

What is the remainder when -3 is tested as a zero using synthetic division?

• -42

• 0

• 42

• -3

What is the remainder when 3 is tested as a zero using synthetic division?

• 0

• -3

• -42

• 42

What happens when a zero is found using synthetic division?

• The polynomial is simplified.

• The polynomial is completely factored.

• The polynomial is broken into factors.

• The polynomial is graphed.