Polynomial Inequalities and Interval Notation

The video tutorial explains how to solve a polynomial inequality by setting the equation to zero, factoring the polynomial, and finding its zeros. It then demonstrates plotting these zeros on a number line and testing intervals to determine which are part of the solution. The tutorial uses a calculator to evaluate the polynomial at test points, graphing the solution, and expressing it using inequalities and interval notation. Finally, it verifies the solution by analyzing the graph of the polynomial.

What is the first step in solving a polynomial inequality?

• Set the equation to zero

• Plot the zeros on a number line

• Factor the polynomial

• Select test values

Which of the following is a factor of the polynomial x^4 - 17x^2 + 16?

• x^2 - 16

• x^2 + 4

• x + 2

• x - 3

How many zeros does the polynomial x^4 - 17x^2 + 16 have?

• Two

• Five

• Three

• Four

When plotting zeros on a number line, what type of points are used for a 'greater than' inequality?

• Closed points

• Open points

• Dashed points

• Solid points

What is the purpose of selecting test values in each interval?

• To find the maximum value

• To determine if the interval is part of the solution

• To simplify the polynomial

• To calculate the derivative

Which test value results in a true inequality for the interval x > 4?

• x = 2

• x = -5

• x = 5

• x = 0

What is the result of substituting x = 0 into the polynomial inequality?

• Undefined

• Zero

• False

• True

How is the solution expressed using interval notation for x < -4?

• [-4, ∞)

• (-4, ∞)

• (-∞, -4]

• (-∞, -4)

What does a parenthesis in interval notation indicate?

• The interval is infinite

• The endpoint is included

• The interval is closed

• The endpoint is not included

What does the graph of the polynomial indicate about the solution?

• The solution is where the graph is below the x-axis

• The polynomial is always positive

• The polynomial is always negative

• The solution is where the graph is above the x-axis