Polynomial Functions

Front

What is the degree of a polynomial function?

Back

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

Front

How do you find the zeros of a polynomial function?

Back

To find the zeros of a polynomial function, set the function equal to zero and solve for the variable.

Front

What is a factor of a polynomial function?

Back

A factor of a polynomial function is a polynomial that divides the function without leaving a remainder.

Front

What does it mean if g(-3) = 0 for a polynomial g(x)?

Back

It means that (x + 3) is a factor of g(x).

Front

How do you perform polynomial long division?

Back

Polynomial long division involves dividing the leading term of the dividend by the leading term of the divisor, multiplying the entire divisor by that result, and subtracting from the dividend.

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that if a polynomial f(x) is divided by (x - c), the remainder is f(c).

Front

What is the Factor Theorem?

Back

The Factor Theorem states that (x - c) is a factor of a polynomial f(x) if and only if f(c) = 0.

Front

What are the steps to factor a cubic polynomial?

Back

1. Look for common factors. 2. Use synthetic division or polynomial long division if necessary. 3. Factor the resulting quadratic if possible.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division that is used when dividing by a linear factor.

Front

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

Back

The leading coefficient determines the end behavior of the polynomial function.