Polynomial Sign and Zeros Analysis

The video tutorial explains how to determine the intervals where a polynomial is positive or negative by analyzing its roots and sign changes between consecutive zeros. It begins with a polynomial in factored form and identifies its zeros. The tutorial then demonstrates how to plot these zeros on a graph and evaluate the polynomial's sign over different intervals. By using sample points and understanding the behavior of the polynomial's factors, the video concludes with a general understanding of the polynomial's shape and behavior across intervals.

What is the factored form of the polynomial p(x) discussed in the video?

• x - 3, 2x + 4, x + 2

• x + 3, 2x - 4, x - 2

• x - 2, 2x + 3, x + 4

• x + 2, 2x - 3, x - 4

Why does the sign of a polynomial remain the same between consecutive zeros?

• Because the polynomial has no zeros

• Because the polynomial is always decreasing

• Because the polynomial does not cross the x-axis

• Because the polynomial is always increasing

What are the zeros of the polynomial p(x) as identified in the video?

• x = -2, x = 1.5, x = 4

• x = 2, x = -1.5, x = -4

• x = -3, x = 2, x = -5

• x = 3, x = -1, x = 5

Which interval is considered when x is less than -2?

• x > 4

• x < -2

• x = 0

• x = 2

What is the sign of the polynomial in the interval where x is between -2 and 1.5?

• Zero

• Positive

• Undefined

• Negative

How is the sign of the polynomial determined over an interval?

• By ignoring the zeros

• By assuming the polynomial is always negative

• By assuming the polynomial is always positive

• By checking the sign of the polynomial at a sample point

What is the sign of the polynomial when x is greater than 4?

• Negative

• Undefined

• Positive

• Zero

What is the general shape of the polynomial graph as concluded in the video?

• Constant

• Always decreasing

• Alternating between positive and negative intervals

• Always increasing

Which method is NOT used to determine the sign of the polynomial over an interval?

• Checking the behavior of individual factors

• Using the sign of the factors

• Evaluating the polynomial at a sample point

• Assuming the polynomial is always zero

What happens to the polynomial's sign if it crosses the x-axis?

• It remains the same

• It changes

• It becomes zero

• It becomes undefined