long division synthetic division remainder theorem can only divide by x-a
TRANSCRIPT
NOTES DAY 6.3
• Long Division• Synthetic Division• Remainder Theorem
Can only divide by x-a
Long Division: Divide Factor
3232 23 xxx32 xx2
23 32 xx Subtract by adding the
opposite
0
+ 0
- 2x
- 1
0 + 0-2x + 3-2x + 3
0
X2-1Is 3/2 a root?
Yes because there was no remainder!
Long Division: Divide Factor
22 xx4xx
xx 42 Subtract by adding the
opposite
-5x
- 5
- 2
+
-5x - 20
18
4
18
x
4
185
x
x
Is -4 a root?
No because there was a remainder!
Synthetic Division: Divide Root
3x
2 3 -4 15 -3
2-6
2X2-3x+5Is -3 a root?
Yes because there was no remainder!
-395 0
-15
Synthetic Division: Divide Root
3 -4 2 -1 -1
3-3
3X2-7x+9+ Is -1 a root?
No because there was a remainder!
-779 -10
-9
Remainder Theorem
1 0 -5 4 12-4
1-4
Find f(-4)
Notice f(-4) = the remainder above!!!!!
-41611 -40
-44 160172
Remainder Theorem
2 6 -5 0 -61-1
2-2
Find P(-1)
You can find P(-1) using synth div or substitution
4-4-9 9
9 -9-70
1 2 -11 -12-1
1-1
Factor Now
If you can’t factor then QF or compl the square!
1-1
-12120
340 xx
Not factorablefactoraisxgivenSolve 1
Divide by -1 using synthetic division
Multiply
Add
AddTo Notes!
1 4 -3 -2 1
1 1
You can’t factor so QF or complete the square!5
5 2
20
25)( 2 xxxf
}2
175,1{
x
0234 23 xxxSolve
Not factorableDivide by 1 using synthetic division
Multiply
Add
AddTo Notes! factoraisxgivenSolve 1
222
2
52
2
55
xx
4
25
1
2
2
52
x
4
25
4
8
2
52
x
4
17
2
52
x
2
17
2
5
x