Math 3 Review#2

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 find the remainder when dividing a polynomial by a linear binomial?

Back

To find the remainder when dividing a polynomial f(x) by (x - c), evaluate f(c).

Front

What is the value of f(-2) for the polynomial f(x) = x^3 - 1?

Back

f(-2) = (-2)^3 - 1 = -8 - 1 = -9.

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 of the form (x - c).

Front

What is the inverse of a function?

Back

The inverse of a function f(x) is a function that reverses the effect of f, denoted as f^(-1)(x). If f(a) = b, then f^(-1)(b) = a.

Front

How do you find the inverse of a linear function?

Back

To find the inverse of a linear function y = mx + b, swap x and y and solve for y: y = (x - b)/m.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements, meaning f(a) = f(b) implies a = b.

Front

What is the significance of the point f(-1)?

Back

The value f(-1) represents the output of the function f when the input is -1, which can be critical for understanding the function's behavior.

Front

How do you evaluate a polynomial at a specific point?

Back

To evaluate a polynomial at a specific point, substitute the value of the variable into the polynomial and simplify.

Front

What is polynomial long division?

Back

Polynomial long division is a method for dividing a polynomial by another polynomial of equal or lower degree, similar to numerical long division.