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Rechner für die synthetische Division

Synthetische Division Schritt für Schritt durchführen

Der Rechner dividiert das Polynom durch das Binom mit Hilfe der synthetischen Division, wobei die Schritte angezeigt werden.

Zugehöriger Rechner: Rechner für lange Polynomdivisionen

Divide (dividend):

By (divisor):

A binomial (of the form ).

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Solution

Your input: find 2x3+x213x+6x2 using synthetic division.

Write the problem in a division-like format.

To do this:

  • Take the constant term of the divisor with the opposite sign and write it to the left.
  • Write the coefficients of the dividend to the right.

x3x2x1x0221136

Step 1

Write down the first coefficient without changes:

2211362

Step 2

Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

22113622=421+4=5

Step 3

Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

221136425=1025(13)+10=3

Step 4

Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

2211364102(3)=62536+(6)=0

We have completed the table and have obtained the following resulting coefficients: 2,5,3,0.

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

Thus, the quotient is 2x2+5x3, and the remainder is 0.

Therefore, 2x3+x213x+6x2=2x2+5x3+0x2=2x2+5x3

Answer: 2x3+x213x+6x2=2x2+5x3+0x2=2x2+5x3