How do you find a solution using synthetic division?

You can utilize synthetic division when dividing a polynomial function by factorial of the type x – c. 

We can utilize this to find difficult problems like X6 Solution in mathematics. The first is the actual quotient and leftover obtained from dividing the polynomial function by x – c. Furthermore, the Remainder Theorem states that the rest obtained after synthetic dividing now gives us utilitarian benefits.

Another application is for determining factors and zeros. The Factor Theorem states that if the functioning value is 0 at a given value c, then x – c is a factor, and c is a zero. 

Synthetic division is being used to identify that value, but the divisions discovered may also help with scaling. It looks that synthetic divisions can help us with a wide range of questions.

Synthetic Division Method

Synthetic division is a shortcut, a polynomial division that only works in the exceptional scenario of dividing by a linear factor. Synthetic division is commonly used to identify polynomials’ zeroes (or roots) rather than dividing out elements.

More on that later. The steps for doing synthetic division and obtaining the fraction and remainder are as follows. To better comprehend it, we will use the following expression: 2×3 – 3×2 + 4x + 5) / (x + 2)

  • Check to see if the polynomial is in a proper format.
  • Write the equations in the dividend’s place and the quadratic factor’s zero in the divisor’s place.
  • Reduce the first factor.
  • Multiply it by the divide and write the result below the next factor.
  • Add them together and put the result down here.
  • Repeat the first two stages until you reach the last level.
  • Separate the last component obtained as a result, which is remaining.
  • To obtain the division, group the equations with the variables.

Therefore, the result obtained after synthetic division of (2×3 – 3×2 + 4x + 5)/(x + 2).

How To Do Synthetic Division In An Easy Way?

Synthetic division of polynomials is a method of calculating polynomials that would not involve factors. Instead of dividing, we multiple, and instead of subtracting, we add.

  1. Dividend coefficients should be written, and the quadratic factor’s zero should be used in place of the divide.
  1. Bring down the first factor and multiply it by the divisor.
  1. Substitute the product for the second variable and add the column.
  1. Continue until you reach the last factor. The final number is used as the remainder.
  1. Write the quotient using the coefficients.
  1. It is worth noting that the resulting polynomial is one degree lower than the dividend polynomial.


Synthetic division is a shortened method for reducing a polynomial by a binomial of the form (x + c) or (x – c). By separating the factors, we may simplify the division. When the divider is a linear factor, the synthetic division is employed to perform the division operation on polynomials.

One benefit of utilizing this method over the standard long technique is that the synthetic division lets you compute without writing variables while completing the polynomial split, making it a simpler method than basic math.