Chapter 8.4, Problem 6WE

To determine

To divide : the given polynomial by the binomial using synthetic division.

Answer to Problem 6WE

  $\frac{2u^4-5u^3-12u^2+2u-8}{u-4}=2u^3+3u^2+2$

Explanation of Solution

Given information :

The polynomial: $2u^4-5u^3-12u^2+2u-8$

The binomial: $u-4$

Formula used : The divisor in a synthetic division is a binomial of the form $x-c$ .

Calculation :

As per the problem,

The dividend is $2u^4-5u^3-12u^2+2u-8$

Since the divisor is $u-4$ , use $4$ for c . Note that the coefficient of $u^4$ is $2$

  $\begin{array}{l}\overline{)4}\text{ 2 }-5-12\text{ 2 }-8\\ \underset{\_}{\text{ 8 12 0 8}}\\ \text{ 2 3 0 2 | 0}\end{array}$

The quotient is $2u^3+3u^2+2$ , and the remainder is $0$

Therefore,

  $\frac{2u^4-5u^3-12u^2+2u-8}{u-4}=2u^3+3u^2+2$