1. 2# Long Division Polynomials

2. Teaching note Show video Long Division vs. Synthetic Division
Show students what they are working towards

3. Common Core objectives:
* Students will be able to use long division to divide polynomials by other polynomials. Use synthetic division to divide polynomials by binomials of the form (x – k). Use the Remainder Theorem and the Factor Theorem.
* Teacher will instruct students to learn about the process of division. Learn about a couple of theorems to help in factoring and solving higher level polynomials

4. Polynomials vocabulary Synthetic Division 1. 2. 3. Long Division 1. 2.
Graphic
Organizer
vocabulary
Division of
Polynomials
Synthetic
Division 1. 2. 3.
Long
Division 1. 2. 1. 2. 3. 4.

5. vocabulary Roots Zeros Rational Root Theorem Remainder Theorem
Due
Test Day
Roots
Zeros
Rational Root Theorem
Remainder Theorem
Factor Theorem
Synthetic Division
Prime Factors
vocabulary

6. What does it mean to factor a number into its prime factors?
what times what equals …

7. Simple Division 3x y z + 12xyz – 4xy z
yesterday
3x y z + 12xyz – 4xy z 3xyz 3 2 3 2
Simple Division
3x y z + 12xyz – 4xy z 3 2 3 2
3xyz xyz xyz

8. Long Division is very similar to Polynomial Division

9. Long Division 18 8 6 5 2597 3 3 2597 5 9 7 -( ) 24 1 9 -( ) 1 7 -( )
Will 3 go into 2? NO
2597 3 5
9 7
-( ) 24
Will 3 go into 25? YES 1 9
-( ) 18 1 7
-( ) 15 2

10. Polynomial Division 3x+13x -5x +10x - 3 -( ) -( ) -2x +4 3x +1x --7
3x+1 2
-2x +4 x 3 2
3x+13x -5x +10x - 3 3 2
-( )
3x +1x - 2
-6x + 10x
Look at 1st term 2 3
-( ) +
-6x - 2x +
3x( ?? ) = 3x x2
12x - 3
-( )
12x + 4 - -7

11. example Think Think Think Multiply: 6x2(x – 2). Subtract.

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

13. Polynomial Division
-( )
-( )
-( )

14. Try This
Answer:

15. *****application
Long Division worksheet
Due next class