## Polynomials

by John Moshman
## 1. Vocabulary

### 1.1. End behavior

1.1.1. What is going on at the ends of each graph.

### 1.2. Leading coefficient

1.2.1. The numbers written in front of the variable with the largest exponent.

### 1.3. Local maximum

1.3.1. The greatest value in a set of points.

### 1.4. Local minimum

1.4.1. The least value in set of points.

### 1.5. Monomial

1.5.1. Consisting of one term

### 1.6. Multiplicity

1.6.1. A large number

### 1.7. Polynomial

1.7.1. is the sum of one or more monomials with real coefficients and non negative integer exponents.

### 1.8. Polynomial function

1.8.1. real numbers and n are a non negative integer.

### 1.9. Synthetic division

1.9.1. A shorthand, or shortcut, method of polynomial division in the case of dividing by a linear factor.

### 1.10. Turning point

1.10.1. a time at which a decisive change in a situation occurs

## 2. Transforming polynomial function

### 2.1. Vertical=f(x)+K

### 2.2. Horizontal=F(x+h)

### 2.3. Vertical stretch=Af(x)

## 3. Investigating graphs of polynomial functions

### 3.1. Linear graph=degree 1

### 3.2. Quadratic graph=degree 2

### 3.3. Cubic graph=degree 3

### 3.4. Quartic graph=degree 4

### 3.5. Quintic graph=degree 5

## 4. Finding real roots of polynomial equations.

### 4.1. Use the zero product property tot find the zeros or solutions.

## 5. Fundamental theorem of algebra.

### 5.1. Use the Zero product property to find the solutions of the numbers and then factor the solutions.

## 6. Dividing polynomials

### 6.1. You can either use long term division or synthetic division

## 7. Factoring polynomials

### 7.1. X-A must equal 0 so to see if the given binomial is a factor of the polynomial you use synthetic substitution and if it equals 0 then it is a factor.

## 8. Identifying the leading coefficient and the degree of a polynomial

### 8.1. 5x^3+15

8.1.1. The Leading coefficient would be 5 and the degree would be 3

## 9. Multiplying and monomial and a polynomial

### 9.1. (x+2)(x^2+3x+5)

9.1.1. You multiply x by everything in the other parenthesis and then multiply 2 by everything in the other parenthesis and then you combine like terms.