Synthetic division

Definition

Synthetic division is a simplified method of dividing a polynomial by a binomial of the form $(x - c)$. It uses only the coefficients of the polynomials and reduces the computational complexity compared to long division.

5 Must Know Facts For Your Next Test

1. Synthetic division can only be used when dividing by a linear divisor of the form $(x - c)$.
2. The process involves writing down only the coefficients of the polynomial, simplifying calculations.
3. You must bring down the leading coefficient as it is, then multiply it by $c$ and add it to the next coefficient iteratively.
4. The final row gives you the coefficients of the quotient polynomial, with any remainder appearing at the end.
5. Synthetic division is particularly useful for finding roots or zeros of polynomial functions.

Review Questions

• What type of divisor must be used for synthetic division to be applicable?
• How do you handle coefficients in synthetic division?
• What does the final row in synthetic division represent?

Related terms

Polynomial Long Division: A traditional method for dividing one polynomial by another, involving multiple steps similar to arithmetic long division.

Remainder Theorem:

A theorem stating that if a polynomial $f(x)$ is divided by $(x - c)$, the remainder is $f(c)$.

Factor Theorem:

A theorem stating that $c$ is a root of a polynomial $f(x)$ if and only if $(x - c)$ is a factor of $f(x)$.