# How to solve (1 4 5 4) synthetic division

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2014-08-04T19:29:20+05:30

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Polynomial is x³ + 4 x² + 5x + 4
Let us divide this polynomial by x + 2  using sythetic division method.
1. Write -2  (-2 comes from x + 2 ) to the left of polynomial coefficients.
2. write 1 the highest coefficient directly below the line . Multiply -2 & 1 and write
the result below 4.
3. add -2 & 4 write result under the line.
4, multiply -2 & 2 and write result below 5.
5. add 5 & -4. write result below line
6 multiply -2 & 1 write result below 4

-2   |    1    4      5      4
|         -2    -4      -2
================
1    2    1        2

Since last addition result is 2. X+2 does not divide given polynomial exactly.
The numbers below the line are understood as 1. x² + 2 x + 1  (polynomial of degree one less than we started with).  last number 2 is reminder.

Given polynomial can be expressed as
(x+2) (x²+2x+1)  +  2