Chapter 4.3, Problem 11E

To determine

To find: the division using synthetic division.

Answer to Problem 11E

The result is $x+12+\frac{49}{x-4}$ .

Explanation of Solution

Given information:

Given expression,

  $\left(x^2+8x+1\right)÷\left(x-4\right)$

Calculation:

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

Because the divisor is $x-4$ , so $k=4$ . Write 4 to the left vertical bar.

Bring down the leading coefficient. Multiply the leading coefficient by the 4. Write the product under the second coefficient then add.

Multiply the previous sum 12 by 4. Write the product under the third coefficient then add. Repeat this process for the remaining coefficient.

  $\begin{array}{cccc}4& 1& 8& 1\\ & & 4& 48\\ & 1& 12& 49\end{array}$

The quotient is $x\left(1\right)+12=x+12$ and remainder is 49.

Therefore, the result is $x+12+\frac{49}{x-4}$ .