Synthetic Division Examples

Example :

Find the resultant polynomial equation using the synthetic division method for p(x) : 3x⁴ + 2x³ - 123x² -126x + 1080 and q(x): x + 2 .

Given :

p(x): 3x⁴ + 2x³ - 123x² -126x + 1080
q(x): x + 2

Solution:

Step 1:

Bring the first coefficient down below the horizontal line.
(i.e) [ 2 x 0 = 0]
Adding 3 and 0, gives 3.

Step 2:

Multiply the divisor (here -2) with the number below horizontal line (here 3) and write it down below the next coefficient.
(2 x - 3 ) = -6

Step 3 :

Add 2 and -6 and write down the next coefficient below the horizontal line.
2 - 6 = -4

Step 5:

Multiplying divisor -2 and -4, we get 8.
Write down 8 below the next coefficient.
Again adding 8 and -123, we get - 115.

Step 6:

Follow the previous steps for all coefficients,

Step 7:

Step 8:

Result:

Therefore, the polynomial value of the given p(x) as calculated using the synthetic division example is 3x³ - 4x² - 115x + 104 + 872 / (x +2)