2# Long Division Polynomials

Polynomials

vocabulary

Long Division

1.2.

SyntheticDivision

1.2.3.

Graphic

Organizer

1.2.3.4.

Divisionof

vocabulary

Roots

Zeros

Rational Root Theorem

Remainder Theorem

Factor Theorem

Synthetic Division

Prime Factors

Due

Test Day

What does it mean to factor a number into its prime factors?90 462

what times what equals …

3x y z + 12xyz – 4xy z3xyz

Simple Division

3x y z + 12xyz – 4xy z

3 2 23

3 2 3 2

3xyz 3xyz 3xyz

yesterday

Polynomial Division

13

31053 23

x

xxx

Long Division is very similar to Polynomial Division

Long Division

2597

3

3 2597Will 3 go into 25? YES

Will 3 go into 2? NO5

8

24-( )

1

9 7

9

6

18-( ) 1

7

5

15-( )

2

23

Polynomial Division

3x+13x -5x +10x - 313

31053 23

x

xxx 23

Look at 1st term

3x( ?? ) = 3x3

x2

3x +1x3 2

-( )

-

-6x + 10x2

-2x

-6x - 2x2

-( )+ +

12x - 312x + 4

+4

-( ) -7

-7 3x+1

-

x2

exampleThink

Think

Think

Multiply: 6x2(x – 2).

Subtract.

Multiply: 2(x – 2).

Subtract.

Multiply: –7x(x – 2).

Subtract.

Polynomial Division

Notice that there is no x term. However, we need to include it when we divide.

52

1592 23

x

xx

159252 23 xxx x0

Polynomial Division

159252 23 xxx

2x

23 52 xx 24x x0

x2

xx 104 2 x10 15

5

x10 25

10

52

10

x

x0-( )

-( )

-( )

Try This

Answer:

2

349105 234

x

xxxx

1743 23 xxx

*****application

Long Division worksheet

Due next class