Characteristics of Polynomials in Standard Form

Front

What determines the end behavior of a polynomial function?

Back

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.

Front

What is the leading coefficient in a polynomial written in standard form?

Back

The leading coefficient is the coefficient of the first term in a polynomial written in standard form.

Front

Identify the leading coefficient of the polynomial f(x) = -2x^4 + 3x^2 - 5.

Back

The leading coefficient is -2.

Front

What is another term for the roots of a polynomial function?

Back

Zeros.

Front

How do you determine the degree of a polynomial?

Back

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

Front

What is the degree of the polynomial 5x^3 - 4x + 2?

Back

The degree is 3.

Front

If a polynomial has a leading coefficient of 0, what can be said about its degree?

Back

If the leading coefficient is 0, the polynomial is not a valid polynomial function.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written as a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n is the leading coefficient.

Front

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

Back

The leading coefficient is 4.

Front

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

Back

If a polynomial has an even degree, its end behavior will be the same on both ends (either both up or both down).