Synthetic division of polynomials Calculator

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Example

Created on 2024-06-20Asked by Elizabeth Roberts (Solvelet student)

Use synthetic division to divide

2x^3 + 3x^2 - 5x + 6

x - 2

Solution

To use synthetic division to divide

2x^3 + 3x^2 - 5x + 6

x - 2

: 1. **Set up synthetic division:**

\begin{array}{r|rrrr} 2 & 2 & 3 & -5 & 6 \\ \hline & 2 & 7 & 9 & 24 \\ \end{array}

2. **Perform the division:**

\begin{array}{r|rrrr} 2 & 2 & 3 & -5 & 6 \\ \hline & & 4 & 14 & 18 \\ \hline & 2 & 7 & 9 & 24 \\ \end{array}

3. **Result:** The quotient is

2x^2 + 7x + 9

with a remainder of

24

. Solved on Solvelet with Basic AI Model

Some of the related questions asked by William Rodriguez on Solvelet

1. Use synthetic division to divide the polynomial

f(x) = x^3 + 2x^2 - 5x - 6

by the linear factor

(x - 2)

.2. Find all the roots of the polynomial equation

g(x) = x^3 - 3x^2 - 4x + 12

using synthetic division.,

DefinitionPolynomials can also be divided using synthetic division instead of long division which is an easier way to divide a polynomial by a linear divisor of the form x−c. For example, suppose that you want to find the quotient and the remainder when you divide 2x3−6x2+2x−1 by x−3.

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