Synthetic Division Calculator
'Cuemath's Synthetic Division Calculator' is an online tool that helps to calculate the quotient and remainder using the synthetic method.
What is Synthetic Division Calculator?
Cuemath's online Synthetic Division Calculator helps you to calculate the quotient and remainder using the synthetic method within a few seconds.
How to Use Synthetic Division Calculator?
Please follow the below steps to use the synthetic division method:
- Step 1: Enter the polynomials in the given input box
- Step 2: Click on the "Divide" button to calculate the quotient and remainder for given polynomials.
- Step 3: Click on "Reset" to clear the field and calculate the quotient and remainder for different polynomials.
What is Synthetic Division?
When we divide a polynomial p(x) by a linear factor x−a (which is a polynomial of degree 1), Q(x) is the quotient polynomial and R(the constant term) is the remainder.
p(x) / (x - a) = Quotient + (Remainder / (x−a)) = Q(x) + R / (x - a)
Steps to use synthetic division method:
- Write the coefficients of the dividend and use the zero of the linear factor in the divisor's place.
- Bring the first coefficient down and multiply it with the divisor.
- Write the product below the 2nd coefficient and add the column.
- Repeat until the last coefficient. The last number is taken as the remainder.
- Take the coefficients and write the quotient.
- Note that the resultant polynomial is of one order less than the dividend polynomial.
Let's see the below example to understand briefly
Solve (2x2 + 3x + 1) / (x + 1)
Similarly, you can try the calculator to find the quotient and remainder using the synthetic division method for
a) (x4 + 5x3 - 3x2 + 2x -8) / (x - 2)
b) (x3 - 5x + 2) / (x + 5)