Chapter 4.4, Problem 69E

To determine

To find: the method which is preferable.

Answer to Problem 69E

The preferred method is used to factor theorem and synthetic division.

Explanation of Solution

Given information:

Given function,

  $g\left(x\right)=x^3-7x^2-4x+28$

First method to find $g\left(7\right)$ is synthetic division and factor theorem. Second method to find is direct substitution.

Calculation:

The factor theorem states that “A polynomial has a factor $x-k$ is and only if $f\left(k=0\right)$ ”.

Because direct substitution requires evaluating exponent and calculator is not allowed. So the preferred method is used to factor theorem and synthetic division.