Chapter 8.4, Problem 5WE

To determine

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

Answer to Problem 5WE

  $\frac{t^4+5t^3-2t-7}{t+5}=t^3-2+\frac{3}{t+5}$

Explanation of Solution

Given information :

The polynomial: $t^4+5t^3-2t-7$

The binomial: $t+5$

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

Calculation :

As per the problem,

The dividend is $t^4+5t^3-2t-7$ . Insert the missing term $0t^2$ .

Since the divisor is $t+5=t-(-5)$ , use $-5$ for c .

  $\begin{array}{l}\overline{)-5}\text{ 1 5 }0-2-7\\ \underset{\_}{-5\text{ 0 0 10}}\\ \text{ 1 0 0 }-2\text{ | 3}\end{array}$

The quotient is $t^3-2$ , and the remainder is $3$

Therefore,

  $\frac{t^4+5t^3-2t-7}{t+5}=t^3-2+\frac{3}{t+5}$