Understanding Polynomial Zeros

The video tutorial explains how to find all zeros of a degree 3 polynomial function. It begins by identifying possible rational zeros using the Rational Zeros Theorem and then graphing the function to find real zeros. The tutorial demonstrates factoring the polynomial using known zeros and performing synthetic division. Finally, it uses the quadratic formula to find the remaining zeros, providing a comprehensive approach to solving polynomial equations.

What is the Rational Zeros Theorem used for?

• Calculating the derivative of a polynomial

• Determining the leading coefficient

• Listing possible rational zeros of a polynomial

• Finding the degree of a polynomial

What are the possible rational zeros for the polynomial with constant term 2 and leading coefficient 1?

• +/- 1, +/- 2

• +/- 3, +/- 4

• +/- 7, +/- 8

• +/- 5, +/- 6

Why do we graph the polynomial function?

• To determine the degree

• To find the derivative

• To identify the x-intercepts

• To calculate the integral

What is the significance of the x-intercept at x = -2?

• It is the minimum value

• It is a turning point

• It is a zero of the function

• It is the maximum value

What method is used to factor the polynomial after identifying a zero?

• Integration

• Differentiation

• Long division

• Synthetic division

What is the remainder when using synthetic division with x = -2?

• 1

• 2

• 0

• -1

Why is the quadratic formula used in this context?

• To find the derivative

• To graph the polynomial

• To integrate the function

• To solve the quadratic factor

What are the values of a, b, and c in the quadratic formula for this problem?

• a = 2, b = -5, c = 3

• a = 1, b = -6, c = 1

• a = 4, b = -3, c = 1

• a = 3, b = -4, c = 2

What is the simplified form of the square root of 32?

• 6 square root 4

• 7 square root 5

• 5 square root 3

• 4 square root 2

What are the two remaining zeros of the cubic function?

• x = 5 +/- 4 square root 4

• x = 6 +/- 5 square root 5

• x = 4 +/- 3 square root 3

• x = 3 +/- 2 square root 2