Polynomial Functions and Their Properties

The video tutorial covers polynomial forms, including standard and factored forms, and how to classify them by degree and terms. It explains factoring and expanding polynomials, using synthetic and long division, and applying the remainder theorem. The tutorial also includes graph analysis, focusing on zeros, y-intercepts, and relative minima and maxima.

What is the process of converting a polynomial from factored form to standard form called?

• Factoring

• Expanding

• Simplifying

• Reducing

Which property is used to expand a polynomial?

• Identity Property

• Associative Property

• Commutative Property

• Distributive Property

How do you classify a polynomial with a degree of 3?

• Linear

• Quadratic

• Cubic

• Quartic

What is the multiplicity of a zero if the factor is repeated twice?

• 1

• 4

• 2

• 3

What is the first step in factoring a polynomial?

• Expanding

• Simplifying

• Dividing

• Identifying common factors

When writing a polynomial in standard form, what should be the order of terms?

• Ascending order of degree

• Descending order of degree

• Random order

• Alphabetical order

What is the purpose of synthetic division?

• To find the remainder

• To factor polynomials

• To classify polynomials

• To expand polynomials

In long division of polynomials, what do you do after subtracting the product from the dividend?

• Add the next term

• Multiply by the divisor

• Divide by the divisor

• Bring down the next term

What does the remainder theorem help determine?

• The factors of the polynomial

• The degree of the polynomial

• The remainder when a polynomial is divided

• The zeros of the polynomial

What does a zero with a multiplicity of 2 indicate on a graph?

• The graph has a horizontal asymptote

• The graph crosses the x-axis

• The graph touches and bounces off the x-axis

• The graph has a vertical asymptote