REMAINDER THEOREM, FACTOR, & SYNTHETIC DIVISION.

Front

What is the Remainder Theorem?

Back

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

Front

Define a factor of a polynomial.

Back

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

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a binomial of the form (x - c).

Front

How do you determine if (x - c) is a factor of f(x)?

Back

If f(c) = 0, then (x - c) is a factor of f(x).

Front

What is the degree of a polynomial?

Back

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

Front

What is the maximum number of x-intercepts for a polynomial of degree n?

Back

A polynomial of degree n can have at most n x-intercepts.

Front

What does the end behavior of a polynomial depend on?

Back

The end behavior of a polynomial depends on its leading term and its degree.

Front

How do you perform synthetic division?

Back

To perform synthetic division, write the coefficients of the polynomial, use the value of c, and follow the synthetic division process.

Front

What is the result of dividing 2x^3 - 5x^2 + 3x + 7 by x - 2?

Back

The result is 2x^2 - x + 1 + 9/(x - 2).

Front

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

Back

The leading coefficient determines the direction of the polynomial's end behavior.