# Synthetic division | Polynomial and rational functions | Algebra II | Khan Academy | Summary and Q&A

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August 1, 2012
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Synthetic division | Polynomial and rational functions | Algebra II | Khan Academy

## TL;DR

Synthetic division is a technique used to simplify polynomial expressions, offering advantages such as speed and space efficiency compared to traditional long division.

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### Q: What is synthetic division?

Synthetic division is a technique used to simplify polynomial expressions by dividing a polynomial of degree 3 or higher by a polynomial of degree 1. It is a faster and more space-efficient alternative to traditional long division.

### Q: What are the requirements for using synthetic division?

The polynomial in the denominator must have a coefficient of 1 and be of degree 1. If the coefficient is different or the degree is higher, additional steps are required for synthetic division.

### Q: How is synthetic division performed?

Synthetic division involves writing the coefficients of the numerator polynomial and the negative of the coefficient of the denominator polynomial. Multiplication, addition, and moving down the row of coefficients are performed to simplify the expression.

### Q: What are the advantages of synthetic division?

Synthetic division is faster and uses less paper space compared to traditional long division. It offers a more algorithmic approach for simplifying polynomial expressions.

## Summary & Key Takeaways

• Synthetic division is a method used to simplify polynomial expressions by dividing a polynomial of degree 3 or higher by a polynomial of degree 1.

• The basic form of synthetic division requires the polynomial in the denominator to have a coefficient of 1 and be of degree 1.

• To perform synthetic division, the coefficients of the numerator polynomial are written and the negative of the coefficient of the denominator polynomial is used. The process involves multiplication, addition, and moving down the row of coefficients.