Synthetic Division Calculator

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Synthetic division calculator is used to divide polynomial by first degree polynomial. This simplified method helps to perform polynomial long division with less writing and calculations. It uses only the coefficients of the terms. This helps to find the remainder when we divide the given polynomial by x-c.

Example 1: Using synthetic division calculator solve;

p(x) = 5x2 + 3/10x + ¼

q(x) = x+5

Write the coefficients of p(x). Find the value for x from q(x)

x+5 =0 ; x= -5

Bring down the 1st coefficient and multiply it with -5 (-5x5= - 25). The answer is written below the 2nd coefficient. Add down the column. (3/10 + -25= -247/10).  Repeat.

-5 [5,   3/10,     1/4]
-25      247/2
------------------------
5,  -247/10,  495/4

Answer : 5x - 247/10 , remainder 495/4

Example 2: Using synthetic division calculator find out if q(x) is a factor of p(x).

p(x)= 2x2 + 3x + 1

q(x)= x+2

Write the coefficients of p(x). Find the value for x from q(x)

x+2=0; x= -2

1st coefficient is multiplied it with -2 (-2x2= - 4). -4 is written below 3. Add down the column. (3+ -4= -1).  Repeat.

-2 [2,   3,   1]
-4    2
----------------
2,  -1,   3

Since remainder (3) is not zero, q(x) is not a factor of p(x)