Long Division and Synthetic division

3 term polynomial

trinomial

T or F Long division of polynomials is similar to long division of whole numbers.

True

n = 0

Constant

N = 3

Cubic

How do we write the result?

Divident/divisor = quotient + remainder/divisor

N = 1

Linear

What is the first thing we must see when dividing polynomials?

Make sure each term is represented

A ___ is a sum or difference of terms. Polynomials have special names based on their ___ and the number of ___they have.

Polynomial Degree Terms

N = 2

Quadratic

N = 4

Quartic

N = 5

Quintic

The graph of a polynomial has to be ___ and ___

Smooth, continuous

Use ___ ___ when a polynomial of degree 1 or higher is divided by x-c .

Synthetic Division

A trick for dividing polynomials

Synthetic division

Helps us solve for the roots of polynomials

Synthetic division

Only works when we divide by 1st degree (linear) polynomials

Synthetic division

T or F If the divisor isn

True

Can only be used when the divisor is in the form

X-c

2 term polynomial

binomial

When you divide the polynomial by one of the binomial factors , the quotient is called a ___ ___ .

depressed equation

How do we check when dividing polynomials

dividend = (quotient • divisor) + remainder

If a polynomial f(x) is divided by x-a, the remainder is the constant ___ , and Dividend=quotient *divisor +remainder

f(a)

1 term polynomial

monomial