Chapter 5.6, Problem 56ES

To determine

Explanation:

Given:

In the given exercise “ $\left(x^7-128\right)÷(x-2)$ ” divide using synthetic division.
When we have to divide a polynomial function by a binomial of the form $(x-c)$ , then we have to use synthetic division. Set up the synthetic division by taking the divisor (what we are dividing by) goes on the outside of the box. The dividend (what we are dividing into) goes on the inside of the box. When we write out the dividend make sure that we write it in descending powers and insert $0\text{'}s$ for any missing terms. Then bring down the leading coefficient to the bottom row by adding zero to it. Then, multiply $c$ by the value just written on the bottom row. Add the column created by writing the sum in the bottom row. Repeat this until done. The numbers in the last row make up our coefficients of the quotient as well as the remainder. The final value of the right is the remainder. Working right to left, the next number is our constant, the next is the coefficient for $x$ , the next is the coefficient of $x^2$ , and so on.