Chapter 4.3, Problem 15E

To determine

To find: the division using synthetic division.

Answer to Problem 15E

The result is $x+3+\frac{18}{x-3}$ .

Explanation of Solution

Given information:

Given expression,

  $\left(x^2+7\right)÷\left(x-3\right)$

Calculation:

Write the coefficient of the dividend in order of descending exponents. Use 0 for the missing $x$ term.

Because the divisor is $x-3$ , so $k=3$ . Write $3$ to the left vertical bar.

Bring down the leading coefficient. Multiply the leading coefficient by the 3. Write the product under the second coefficient then add.

Multiply the previous sum 3 by 3. Write the product under the third coefficient then add. Repeat this process for the remaining coefficient.

  $\begin{array}{cccc}3& 1& 0& 9\\ & & 3& 9\\ & 1& 3& 18\end{array}$

The quotient is $x\left(1\right)+3=x+3$ and remainder is 18.

Therefore, the result is $x+3+\frac{18}{x-3}$ .