Degree and Leading Coefficients of Polynomials

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

How can you determine if the degree of a polynomial is even or odd?

Back

You can determine if the degree is even or odd by observing the behavior of the polynomial's ends: if both ends point the same way, the degree is even; if they point in opposite directions, the degree is odd.

Front

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

Back

If a polynomial has an even degree, it means that as the input values approach positive or negative infinity, the output values will also approach positive infinity.

Front

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

Back

If a polynomial has an odd degree, it means that as the input values approach positive infinity, the output values will approach positive infinity, and as the input values approach negative infinity, the output values will approach negative infinity.

Front

What is a leading coefficient in 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 graph of a polynomial?

Back

The leading coefficient determines the direction of the graph's ends: if it is positive, the right end of the graph goes up; if it is negative, the right end goes down.

Front

What is the significance of the leading coefficient being positive?

Back

If the leading coefficient is positive, the polynomial will rise to the right, indicating that the function approaches positive infinity as x approaches positive infinity.

Front

What is the significance of the leading coefficient being negative?

Back

If the leading coefficient is negative, the polynomial will fall to the right, indicating that the function approaches negative infinity as x approaches positive infinity.

Front

Can a polynomial have both even and odd degree terms?

Back

Yes, a polynomial can have both even and odd degree terms, but the overall degree of the polynomial is determined by the term with the highest degree.

Front

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

Back

The end behavior will be that both ends of the graph rise to positive infinity.