How to solve (1 4 5 4) synthetic division

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

Written on Feb. 2, 2020, 11:46 p.m.