Understanding Polynomial Zeros

The video tutorial explains how to find all zeros of a degree four polynomial function. It begins by identifying possible rational zeros using the factors of the constant term and leading coefficient. The tutorial then uses graphical analysis to find real zeros, which are the x-intercepts of the graph. These zeros help factor the polynomial, allowing for synthetic division to find a degree two factor. Finally, the quadratic formula is applied to solve the quadratic factor, revealing complex zeros. The tutorial concludes with a summary of the four zeros found: two real and two complex.

What is the maximum number of zeros a degree four polynomial can have?

• Four

• Six

• Eight

• Two

How do we determine the possible rational zeros of a polynomial?

• By listing the factors of the constant term and leading coefficient

• By using the quadratic formula

• By graphing the polynomial

• By using synthetic division

What do the x-intercepts of a polynomial graph represent?

• The maximum points

• The complex zeros

• The minimum points

• The real zeros

If x = -4 is a zero of the polynomial, what is a corresponding factor?

• x - 4

• x - 1

• x + 4

• x + 1

What is the purpose of synthetic division in this context?

• To simplify the polynomial

• To find the degree of the polynomial

• To graph the polynomial

• To find the degree two factor

What is the quadratic formula used for?

• Graphing polynomials

• Solving quadratic equations

• Performing synthetic division

• Finding the factors of a polynomial

What are the values of A, B, and C in the quadratic equation derived from the polynomial?

• A = 1, B = 4, C = -10

• A = 3, B = -2, C = 5

• A = 2, B = -4, C = 8

• A = 1, B = -6, C = 10

What is the result of simplifying 6 +/- 2i all over 2?

• 3 +/- i

• 2 +/- 3i

• 6 +/- i

• 3 +/- 2i

Which of the following is a complex zero of the polynomial?

• x = 1 - i

• x = 2 - i

• x = 4 + i

• x = 3 + i

How many complex zeros does the polynomial have?

• One

• Two

• Three

• Four