2# long division polynomials. teaching note show video long division vs. synthetic division show...
TRANSCRIPT
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
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
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-( )
-( )
-( )