# Synthetic division - PowerPoint PPT Presentation

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## Synthetic division

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### Synthetic division Division of polynomials Synthetic division Set up for: Is (x-4) a factor of 1 2 0 -1 1 The root on the outside and the coefficients ... – PowerPoint PPT presentation

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Title: Synthetic division

1
Synthetic division
• Division of polynomials

2
Synthetic division
• Set up for Is (x-4) a factor of

The root on the outside and the coefficients,
including a zero placeholder
• 1 2 0 -1
• 1

3
Synthetic division
• We multiply the bottom number to the root and add
down..
• 1 2 0 -1
• 4 24 96
• 1 6 24 95

The remainder is 95 so the answer is no!
4
Synthetic Division Determine if 3 is a
root of F(x)
3
10 9 -19 6
Set Up with coefficients

10
5
Determine if 3 is a root
3
10 9 -19 6
Dont forget your remainder should be zero
294
30 117
10 39 98 300
Remainder is 300, so 3 is not a root!
The remainder is 300
6
Determining if -2 is a root-Synthetic Division
-2
10 9 -19 6

10
7
Determining if -2 is a root-Synthetic Division
-2
10 9 -19 6
Dont forget your remainder should be zero YES!
-20 22 -6
(No remainder) so -2 is a root!
10 -11 3 0
8
Using the root to factor the polynomial -2 is
a root, so (x2) is a factor
9
Determining if -2 is a root-Synthetic Division
-2
10 9 -19 6
We can write a factorization here! These are
coefficients of the other factor!
-20 22 -6
10 -11 3 0
10
Factor completely
We can now factor the second factor