Understanding Polynomials

What is a necessary condition for an expression to be considered a polynomial?

• The expression must have at least three terms.

• The coefficients must be integers.

• The exponents must be whole numbers.

• The variables must be only x and y.

Which of the following is NOT a polynomial?

• 3x^4 - 5x^3 + 2

• 1/x + x^2

• x^2 - 4x + 4

• x^3 + 2x^2 - x + 1

What is the standard form of a polynomial?

• When terms are arranged in descending order of exponents.

• When terms are arranged in ascending order of exponents.

• When all terms have the same coefficient.

• When all terms are multiplied together.

Which of the following is a characteristic of a polynomial in factored form?

• Terms are added or subtracted.

• Terms are multiplied together.

• Terms are divided.

• Terms are in ascending order.

What is the degree of the polynomial 2x^3 - 4x^2 + 3?

• 4

• 1

• 2

• 3

What does the degree of a polynomial indicate?

• The number of terms in the polynomial.

• The highest power of the variable.

• The sum of the coefficients.

• The number of x-intercepts.

How does a positive leading coefficient affect the end behavior of a polynomial?

• It causes the graph to decrease on the right.

• It causes the graph to increase on the right.

• It causes the graph to be symmetric.

• It has no effect on the graph.

What is the effect of a negative leading coefficient on a polynomial's graph?

• The graph will be a straight line.

• The graph will have no x-intercepts.

• The graph will always be above the x-axis.

• The graph will end pointing down on the right.

Which polynomial degree results in the graph starting and ending in opposite directions?

• Negative degree

• Even degree

• Zero degree

• Odd degree

Which graph behavior indicates a polynomial with an odd degree?

• Flat line

• One end up and one end down

• Both ends pointing down

• Both ends pointing up