Synthetic Division :
Synthetic Division Synthetic division is a shorthand, or shortcut, method of polynomial division in the special case of dividing by a linear factor -- and it only works in this case.
Synthetic Division includes steps such as:
Making sure all Place Holders are there
The factor changes to a Zero - e.g.(x-3) would be 3
Example of Synthetic Division :
Example of Synthetic Division The sequence of operations in synthetic division may be summarized as follows, using as an example the division of 3x - 4x2 + x4 - 3 by x + 2:
Now You Try: :
Now You Try: Divide 3x3 – 2x2 + 3x – 4 by x – 3 using synthetic division.
Change (x-3) to 3 I 3 -2 3 -4
I
I I_________________________ 3 3 7 24 68 9 21 72
Long Division :
Long Division Long division of a polynomial is like division back in elementary school.
It can be very easy done but yet tricky. You have to remember some steps as well.
Example of Long Polynomial Division :
Example of Long Polynomial Division For example, if 3x4 + 2x3 + 2x2 - x - 6 is to be divided by x - 1, the long form would be as follows:
Now You Try: :
Now You Try: Long Divide x^2-9x-10 by x+1 x +1x _____________ -10x - 10 - 10 -10x -10 ___________ *Change signs to negative *Change signs to positive 0 (-) (-) (+) (+)