POLYNOMIAL FUNCTIONS REVIEW

Front

What are the zeros of the polynomial?

Back

The zeros of the polynomial are the values of x that make the polynomial equal to zero. For example, for the polynomial with zeros at x=5 and x=-3 (with a multiplicity of 2), these are the points where the graph intersects the x-axis.

Front

What is the value of the coefficient in the polynomial −3x + 6?

Back

The coefficient is the number in front of the variable. In this case, the coefficient of x is -3.

Front

How many roots does the polynomial f(x) = 4x^5 - 3x^4 + 2x^2 - 7x + 1 have?

Back

This polynomial has 5 roots, as the degree of the polynomial (the highest power of x) indicates the maximum number of roots.

Front

How many turning points does the graph of P(x) = x^4 - 2x^2 + x + 1 have?

Back

The graph of this polynomial has less than 4 turning points, as the maximum number of turning points is one less than the degree of the polynomial.

Front

Determine the degree of the function f(x) = 2x^3 + x - 5x^5 + 1.

Back

The degree of the function is 5, which is the highest exponent of x in the polynomial.

Front

What is a polynomial function?

Back

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. For example, f(x) = 2x^3 - 4x + 7 is a polynomial function.

Front

What is the leading coefficient of the polynomial f(x) = 3x^4 - 2x^3 + x - 5?

Back

The leading coefficient is the coefficient of the term with the highest degree. In this case, the leading coefficient is 3.

Front

What does it mean for a root to have multiplicity?

Back

Multiplicity refers to the number of times a particular root appears in a polynomial. For example, if x = -3 is a root with multiplicity 2, it means (x + 3)^2 is a factor of the polynomial.

Front

What is the relationship between the degree of a polynomial and its number of roots?

Back

The degree of a polynomial indicates the maximum number of roots it can have. For example, a polynomial of degree 4 can have up to 4 roots.

Front

What is a turning point in the context of polynomial functions?

Back

A turning point is a point on the graph of a polynomial where the direction of the graph changes from increasing to decreasing or vice versa.