Learning to Find All of the Zeros of a Polynomial

The video tutorial covers the process of determining rational and real zeros using synthetic division and the remainder theorem. It explains the importance of these methods in finding factors and zeros of polynomials. The tutorial compares the effectiveness of synthetic division and the remainder theorem, highlighting the benefits of each approach. It concludes with a summary of the key findings and methods discussed.

What is the primary method discussed for determining zeros when a graph is not available?

• Applying the quadratic formula

• Using a calculator

• Using a computer program

• Guessing and checking

Why is synthetic division preferred over the remainder theorem for finding zeros?

• It is more accurate

• It provides both the remainder and the quotient

• It requires less computation

• It is faster

What additional information does synthetic division provide besides the remainder?

• The degree of the polynomial

• The quotient, which is also a factor

• The original polynomial

• The number of zeros

What is the factor form if a zero is found to be 3?

• X + 3

• X - 3

• X/3

• 3X

What is the next step after identifying a factor using synthetic division?

• Graph the polynomial

• Use the quadratic formula

• Set the factor equal to zero to find remaining zeros

• Multiply the factor by the original polynomial

What should be done if a polynomial is not factorable?

• Use a calculator

• Use the quadratic formula

• Try a different method

• Ignore the polynomial

How many positive and negative rational zeros were confirmed in the final section?

• Zero positive and three negative

• Three positive and zero negative

• Two positive and one negative

• One positive and two negative