Synthetic division is a useful tool for quickly dividing polynomials without the need for long division. It is frequently used in calculus to find the roots of a polynomial or simplify a complex expression. But what remainder is represented by the synthetic division below?

What is Synthetic Division?

Synthetic division is a method that can be used to divide polynomials with fewer steps than traditional long division. By using this technique, the divisor can be simplified down to one of its linear factors. This reduces the polynomial expression to a linear equation, which is simpler and quicker to solve.

How Does Synthetic Division Work?

The basis of synthetic division requires that you have a divisor that is a linear polynomial of the form ax + b. To divide two polynomials using this technique, the divisor is written in the left-hand column and the dividend is written on the top row. Then, the process of synthetic division is a pattern of subtracting and dividing that continues until the remainder is reached. The remainder is then written at the bottom of the division.

Which Remainder is Represented by Synthetic Division?

The remainder in synthetic division is represented by the final answer written at the bottom of the division. This answer is the remainder of the original dividend and divisor after completing the synthetic division process. The remainder may be written as a fraction or with the letter “R” written in front of it. As an example, if the synthetic division yields a result of “R-2”, then the remainder is -2.

Conclusion

Synthetic division is a useful tool to quickly divide polynomials without the need for long division. The remainder in synthetic division is represented by the final answer written at the bottom of the division, which may be written as a fraction or with the letter “R” written in front of it. With this technique, complex expressions can be simplified and the roots of polynomials can be found with fewer steps.