Degree and Leading Coefficients of Polynomials

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

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

Back

If the leading coefficient is positive, the right side of the graph goes up. If it is negative, the right side goes down.

Front

What does it mean if a polynomial has an even degree?

Back

A polynomial has an even degree if the highest power of the variable is an even number, resulting in both ends of the graph pointing in the same direction.

Front

What does it mean if a polynomial has an odd degree?

Back

A polynomial has an odd degree if the highest power of the variable is an odd number, resulting in the ends of the graph pointing in opposite directions.

Front

How can you determine the degree of a polynomial?

Back

The degree of a polynomial is determined by the highest exponent of the variable in the polynomial.

Front

What is the significance of the degree of a polynomial in terms of its roots?

Back

The degree of a polynomial indicates the maximum number of roots (real or complex) it can have.

Front

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

Back

Both ends of the graph will rise, meaning as x approaches positive or negative infinity, the polynomial approaches positive infinity.

Front

What is the end behavior of a polynomial with a negative leading coefficient and an even degree?

Back

Both ends of the graph will fall, meaning as x approaches positive or negative infinity, the polynomial approaches negative infinity.

Front

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

Back

The left end of the graph falls while the right end rises, meaning as x approaches negative infinity, the polynomial approaches negative infinity, and as x approaches positive infinity, it approaches positive infinity.

Front

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

Back

The left end of the graph rises while the right end falls, meaning as x approaches negative infinity, the polynomial approaches positive infinity, and as x approaches positive infinity, it approaches negative infinity.