Dividing Polynomials

Intro - Chapter 4.1

Using Long DivisionExample 1:

Dividing Polynomials

DIVISOR

3 22 5 6x x x 2x

DIVIDEND

2x 4x 3

3 22x x24x 5x

3x 6 3 6x

0REMAINDER

QUOTIENT

24 8x x

Example 2: Divide by x x3 22 6

Using Synthetic Division to Divide a Polynomial by a Divisor x – r

x 21 2 0 6 2x 2r

1

4 8 10

COEFFICIENTS OF THE

DIVIDEND

** REMEMBER PLACE

HOLDERS**

COEFFICIENTS OF QUOTIENT REMAINDER

2 8 16

10

2x

The final answer:

21x1 4 8 102 8 16

1 2 0 62

4x 8

It Means …

x x3 22 6 2x 2 4 8x x 10

If is divided by then

Division Algorithm:

xrxqxhxf

xf xh

f x h x q x r x

QUOTIENTDIVIDEND

REMAINDERDIVISOR

If the remainder is 0 then, the __________ and the ______________ are factors of dividend.

If a polynomial is divided by ___________, then the remainder is __________

A polynomial function has a linear factor x – a if and only if ___________

xf

A polynomial of degree n has at most n distinct real ____________________.

Things to RememberDIVISOR

Example3: Find the remainder when is divided by x + 1

53 2479 xx

79 241 3 1 5 1 3 5 7

QUOTIENT

f cx c

0f a

ROOTS OR ZEROS

Let be a polynomial. If r is a real number that satisfies any of the following statements, then r satisfies any of the following statements:

r is a ________ of the function f

r is an ______________ of the graph of the function f

_____ is a solution, or root of the equation ________

___________ is a factor of the polynomial f(x)

ZERO

x intercept

x r

xf

0f x

x r

Asst. #48 Sect 4.1 pg. 248-250#1-8, 9, 18, 22, 23, 28, 39, 45, 47, 50, 51, 57, 59, 61, 64, 69