Understanding Polynomial Functions

The video tutorial explains how to find a degree three polynomial function with given roots of -2, 4, and -6, and a leading coefficient of 1. It covers the formulation of the polynomial using binomial factors, simplifies it to its factored form, and then expands it to its expanded form. The tutorial provides a step-by-step approach to multiplying binomials and combining like terms to achieve the final polynomial expression.

What is the degree of the polynomial function we are asked to find?

• Degree 3

• Degree 2

• Degree 5

• Degree 4

If a polynomial has roots, what do these roots correspond to in the polynomial?

• Binomial factors

• Coefficients

• Constants

• Exponents

What is the form of a polynomial function with roots r1, r2, and r3?

• f(x) = a + (x - r1)(x - r2)(x - r3)

• f(x) = a(x - r1)(x - r2)(x - r3)

• f(x) = a(x * r1)(x * r2)(x * r3)

• f(x) = a(x + r1)(x + r2)(x + r3)

What is the value of 'a' if the coefficient of x cubed is 1?

• 2

• 1

• 0

• 3

How does x minus negative two simplify?

• x - 2

• x + 2

• x * 2

• x / 2

What is the factored form of the polynomial function given the roots?

• (x - 2)(x + 4)(x - 6)

• (x - 2)(x - 4)(x - 6)

• (x + 2)(x - 4)(x + 6)

• (x + 2)(x + 4)(x + 6)

What is the first step in expanding the polynomial function?

• Divide the terms by x

• Add all terms together

• Multiply all terms together

• Multiply the first two binomials

What is the result of multiplying x squared by x?

• x

• x to the fourth

• x squared

• x cubed

What is the expanded form of the polynomial function?

• x cubed - 4x squared - 20x - 48

• x cubed - 4x squared + 20x + 48

• x cubed + 4x squared - 20x - 48

• x cubed + 4x squared + 20x + 48

What is the final step in expanding the polynomial function?

• Combine like terms

• Add coefficients

• Divide by x

• Subtract constants