Degrees of polynomials and Multiplicity

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.

Front

What are the zeros of a polynomial?

Back

The zeros of a polynomial are the values of the variable that make the polynomial equal to zero.

Front

What does it mean if a polynomial has a zero with odd multiplicity?

Back

If a polynomial has a zero with odd multiplicity, the graph of the polynomial will cross the x-axis at that zero.

Front

What does it mean if a polynomial has a zero with even multiplicity?

Back

If a polynomial has a zero with even multiplicity, the graph of the polynomial will touch the x-axis at that zero but will not cross it.

Front

How do you find the zeros of the polynomial y = 3(2x + 4)(x + 1)(x - 3)?

Back

Set each factor equal to zero: 2x + 4 = 0, x + 1 = 0, x - 3 = 0. The zeros are x = -2, x = -1, and x = 3.

Front

What is the factored form of a polynomial?

Back

The factored form of a polynomial expresses it as a product of its factors, which can include linear factors and constants.

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient determines the end behavior of the polynomial's graph.

Front

How do you determine the multiplicity of a zero from a polynomial's factors?

Back

The multiplicity of a zero is determined by the exponent of the factor corresponding to that zero.

Front

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

Back

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

Front

What is the relationship between the degree of a polynomial and the number of zeros it can have?

Back

A polynomial of degree n can have at most n zeros, counting multiplicities.