Polynomial Synthetic division calculator

SolutionHelp

x2-10x+25 $x^2-10x+25$ and

x-5 $x-5$

x3+4x2-4x-16 $x^3+4x^2-4x-16$ and

x-2 $x-2$

x3+6x2+12x+10 $x^3+6x^2+12x+10$ and

x+2 $x+2$

Example

1. Find synthetic division of x2-10x+25 $x^2-10x+25$ and x-5 $x-5$

Solution:

x2-10x+25x-5 $(x^2-10x+25)/(x-5)$ using synthetic division

To determine root divisor, we have to solve divisor equation

x-5=0 $x-5=0$

$:.$ our root becomes

$x=5$

Write coefficients of the dividend

$x^2-10x+25$ to the right and our root

$5$ to the left

$5$	$1$	$-10$	$25$

Step-1 : Write down the first coefficient

$1$

$5$	$1$	$-10$	$25$

	$1$

Step-2 : Multiply our root

$5$ by our last result

$1$ to get

$5$ [

$5$ ×

$1$ =

$5$ ]

$5$	$1$	$-10$	$25$
		$5$
	$1$

Step-3 : Add new result

$5$ to the next coefficient of the dividend

$-10$ , and write down the sum

$-5$ , [

$(-10)$ +

$5$ =

$-5$ ]

$5$	$1$	$-10$	$25$
		$5$
	$1$	$-5$

Step-4 : Multiply our root

$5$ by our last result

$-5$ to get

$-25$ [

$5$ ×

$(-5)$ =

$-25$ ]

$5$	$1$	$-10$	$25$
		$5$	$-25$
	$1$	$-5$

Step-5 : Add new result

$-25$ to the next coefficient of the dividend

$25$ , and write down the sum

$0$ , [

$25$ +

$(-25)$ =

$0$ ]

$5$	$1$	$-10$	$25$
		$5$	$-25$
	$1$	$-5$	$0$

We have completed the table and have obtained the following coefficients

$1,-5,0$

All coefficients, except last one, are coefficients of quotient, last coefficient is remainder.
Thus quotient is

$x-5$ and remainder is

$0$