Chapter 4.3, Problem 18E

To determine

To find: the division using synthetic division.

Answer to Problem 18E

The result is $x^3-x^2+5x-9+\frac{10}{x+5}$ .

Explanation of Solution

Given information:

Given expression,

  $\left(x^4+4x^3+16x-35\right)÷\left(x+5\right)$

Calculation:

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

Because the divisor is $x+5$ , so $k=-5$ . Write $-5$ to the left vertical bar.

Bring down the leading coefficient. Multiply the leading coefficient by the $-5$ . Write the product under the second coefficient then add.

Multiply the previous sum $-1$ by $-5$ . Write the product under the third coefficient then add. Repeat this process for the remaining coefficient.

  $\begin{array}{cccccc}-5& 1& 4& 0& 16& -35\\ & & -5& 5& -25& 45\\ & 1& -1& 5& -9& 10\end{array}$

The quotient is $x^3\left(1\right)+x^2\left(-1\right)+x\left(5\right)-9=x^3-x^2+5x-9$ and remainder is 10.

Therefore, the result is $x^3-x^2+5x-9+\frac{10}{x+5}$ .