Pre Calc Review Unit 5

Front

What is the Remainder Theorem?

Back

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

Front

How do you evaluate a polynomial at a specific value?

Back

To evaluate a polynomial p(x) at x = a, substitute a into the polynomial and simplify.

Front

What does it mean for a polynomial to have a degree of at least n?

Back

A polynomial has a degree of at least n if the highest power of the variable in the polynomial is n or greater.

Front

What is the factored form of a polynomial?

Back

The factored form of a polynomial expresses it as a product of its linear factors.

Front

How do you find the roots of a polynomial equation?

Back

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

Front

What is the significance of the x-intercepts of a polynomial graph?

Back

The x-intercepts of a polynomial graph represent the roots of the polynomial, where the graph crosses the x-axis.

Front

What is synthetic division?

Back

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

Front

What is the relationship between the degree of a polynomial and its number of roots?

Back

A polynomial of degree n can have at most n roots, counting multiplicities.

Front

What is the difference between a polynomial and a rational function?

Back

A polynomial is a function that consists of terms with non-negative integer exponents, while a rational function is a ratio of two polynomials.

Front

How do you determine the end behavior of a polynomial function?

Back

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