Synthetic Division Calculator ·

22 Jul 2024, 00:00

Synthetic Division Calculator Image to Crop

Use synthetic division for:

x3 + 7x2 - 38x - 240
x + 5

Determine our root divisor:

Solve the divisor equation x + 5 = 0
Subtract 5 from each side of the equation to get
x + 5 - 5 = 0 - 5
Therefore, our root becomes x = -5

	1	7	-38	-240
-5

	1	7	-38	-240
-5	↓
	1

Multiply our root -5 by 1
Take -5 and put that in column 2:

	1	7	-38	-240
-5		-5
	1

-5 + 7 = 2
Put this in the answer column 2:

	1	7	-38	-240
-5		-5
	1	2

Multiply our root -5 by 2
Take -10 and put that in column 3:

	1	7	-38	-240
-5		-5	-10
	1	2

-10 + -38 = -48
Put this in the answer column 3:

	1	7	-38	-240
-5		-5	-10
	1	2	-48

Multiply our root -5 by -48
Take 240 and put that in column 4:

	1	7	-38	-240
-5		-5	-10	240
	1	2	-48

240 + -240 = 0
Put this in the answer column 4:

	1	7	-38	-240
-5		-5	-10	240
	1	2	-48	0

Leading Answer Term = x(3 - 1) = x2

Since the last number in our result line = 0, we will not have a remainder and have a clean quotient which is shown below in our answer:

Answer = x2 + 2x - 48

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It appears your answer forms a quadratic equation since the maximum power of your result equation is 2 and your remainder is zero. Click here to solve this quadratic equation

How does the Synthetic Division Calculator work?

Free Synthetic Division Calculator - Using Ruffinis Rule, this performs synthetic division by dividing a polynomial with a maximum degree of 6 by a term (x ± c) where c is a constant root using the factor theorem. The calculator returns a quotient answer that includes a remainder if applicable. Also known as the Rational Zero Theorem
This calculator has 1 input.

What 3 formulas are used for the Synthetic Division Calculator?

For x + a, our root is -1 * a
Write down our coefficients horizontally and our root of a to the left
Multiply root by last result and repeat process

For more math formulas, check out our Formula Dossier

What 4 concepts are covered in the Synthetic Division Calculator?

divisionseparate a number into partspolynomialan expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).ruffinis rulean efficient method of dividing a polynomial by a linear factor, with or without a remainder. synthetic divisiona shorthand method for dividing a polynomial by a linear factor