Chapter A.4, Problem 28AYU

To determine

To find: Do you prefer to use long division or synthetic division?

Does the value of $c$ makes a difference to you in choosing?

Answer to Problem 28AYU

Synthetic division is an easy way to divide polynomials by a polynomial of the form $\left(x - c\right)$. It is both a way to calculate the value of a function at $c$ (Remainder Theorem) as well as to check whether or not $c$ is a root of the polynomial (Factor Theorem). Synthetic division is a shortcut to long division.

Explanation of Solution

Given:

A polynomial $x - c$.

Calculation:

Synthetic division is an easy way to divide polynomials by a polynomial of the form $\left(x - c\right)$. It is both a way to calculate the value of a function at $c$ (Remainder Theorem) as well as to check whether or not $c$ is a root of the polynomial (Factor Theorem). Synthetic division is a shortcut to long division.