Understanding Polynomials and Graphs

What is a polynomial?

• An equation with variables in the exponent

• An equation with variables raised to fractional exponents

• An equation with variables raised to whole number exponents

• An equation with variables in the denominator

Which of the following is NOT a polynomial?

• x^5 - 3x + 2

• 4x^4 - 2x^2 + 7

• x^2 + 1/x

• 2x^3 + 3x^2 - x + 5

What tool can be used to sketch polynomial graphs?

• Google Sheets

• Adobe Photoshop

• Desmos

• Microsoft Word

What does a positive leading coefficient indicate about a polynomial's end behavior?

• The graph decreases to the right

• The graph increases to the right

• The graph decreases to the left

• The graph remains constant

Which graphs have a positive leading coefficient?

• Graphs that decrease to the left

• Graphs that decrease to the right

• Graphs that increase to the right

• Graphs that remain constant

What is the end behavior of a polynomial with an odd degree and a positive leading coefficient?

• Decreases left, increases right

• Increases left, decreases right

• Both ends decrease

• Both ends increase

What does it mean if a polynomial graph 'bounces' at a root?

• The root is a complex number

• The root has an even multiplicity

• The root has an odd multiplicity

• The root is not a real number

How do you find the zeros of a polynomial in factored form?

• Differentiate the polynomial

• Integrate the polynomial

• Multiply all factors

• Set each factor equal to zero

What is the significance of an odd exponent in a polynomial's factor?

• The graph has no real roots

• The graph crosses the x-axis at the root

• The graph bounces at the root

• The graph remains constant at the root

What is the term for the number of times a particular root is repeated in a polynomial?

• Exponent

• Degree

• Coefficient

• Multiplicity