```Question 469097
see the picture below:
<img src = "http://theo.x10hosting.com/problems/synthetic_division_1.jpg" alt = "***** picture not found *****"/ >
Synthetic Division can only be used if the divisor is linear, i.e. (x - 5), x + 6), etc.
You order the dividend from highest exponent to lowest exponent and you just enter the coefficients.
You fill in the blanks, i.e. if it goes from 5x^2 to 7 without an intervening x, then you fill in the blanks to make it 5x^2 + 0x + 7 instead of 5x^2 + 7.
This problem didn't need any blanks to be filled in, so we just wrote down the exponents as is.
you then take your divisor and solve for x to get:
x+4 = 0
x = -4
What you see is the result.
The divisor is on the left and the coefficients of the dividend are on the right.
first bring down the 5.
then multiply 5 by  -4 and put the result under the -1.
then add -1 and -20 to get -21.
then multiply -4 by -21 to get +84.
put the +84 under the -3,
add +84 and -3 to get +81
multiply +81 by -4 to get -324
put the -324 under the +1
add +1 and -324 to get -324.