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Synthetic Division Review
To divide synthetically:
1. The divisor must be a binomial that can be written x – c. Only c is used
from the divisor.
2. The dividend must be written with powers of the variable in descending
order. Only coefficients of the dividend are used and zero (0) is used as a
placeholder for any missing variable term or constant.
The following is an example that demonstrates how to write the problem to
divide synthetically.
(x3 + 4x2 – 8) / (x + 4)
(1x3 + 4x2 + 0x – 8)
x + 4 is the divisor -4 1 4 0 -8 ⇐ Dividend
⇑ -4 0 0
Divisor 1 0 0 -8 ⇐ (-8) Remainder
⇑ ⇑ ⇑
Quotient
We now outline the actual sequence of steps involved when using synthetic
division to solve (2x3 + 3x2 – 4x + 8) / (x + 3)
First, show the divisor and the dividend:
-3 2 3 -4 8
Next, “bring down” the first coefficient of the dividend:
-3 2 3 -4 8
⇓
⇓⇓
⇓________
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