Chapter 4.3, Problem 12E

To determine

To find: the division using synthetic division.

Answer to Problem 12E

The result is $4x-5-\frac{15}{x-2}$ .

Explanation of Solution

Given information:

Given expression,

  $\left(4x^2-13x-5\right)÷\left(x-2\right)$

Calculation:

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

Because the divisor is $x-2$ , so $k=2$ . Write 2 to the left vertical bar.

Bring down the leading coefficient. Multiply the leading coefficient by the 2. Write the product under the second coefficient then add.

Multiply the previous sum $-5$ by 2. Write the product under the third coefficient then add. Repeat this process for the remaining coefficient.

  $\begin{array}{cccc}2& 4& -13& -5\\ & & 8& -10\\ & 4& -5& -15\end{array}$

The quotient is $x\left(4\right)-5=4x-5$ and remainder is $-15$ .

Therefore, the result is $4x-5-\frac{15}{x-2}$ .