Polynomials Part 2

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

Front

What does the degree of a polynomial indicate?

Back

The degree of a polynomial indicates the highest power of the variable in the polynomial.

Front

What is the relationship between the leading coefficient and the end behavior of a polynomial function?

Back

If the leading coefficient is positive and the degree is even, the ends of the graph rise. If it is negative and the degree is even, the ends fall. If the degree is odd, one end rises and the other falls.

Front

What are the zeros of a polynomial?

Back

The zeros of a polynomial are the values of x that make the polynomial equal to zero; they are also known as roots or x-intercepts.

Front

What is the multiplicity of a zero?

Back

The multiplicity of a zero refers to the number of times a particular zero is repeated in a polynomial.

Front

How do you determine the number of real solutions of a polynomial?

Back

The number of real solutions can be determined by analyzing the degree of the polynomial and the nature of its zeros.

Front

What is the difference between rational and irrational solutions?

Back

Rational solutions can be expressed as fractions, while irrational solutions cannot be expressed as simple fractions.

Front

What is the significance of a negative leading coefficient?

Back

A negative leading coefficient indicates that the polynomial will fall to the right as x approaches positive infinity.

Front

What does it mean for a zero to have even multiplicity?

Back

A zero with even multiplicity means that the graph touches the x-axis at that zero but does not cross it.

Front

What does it mean for a zero to have odd multiplicity?

Back

A zero with odd multiplicity means that the graph crosses the x-axis at that zero.