Chapter 6, Problem 5QC

To determine

To Simplify :

The given expression by using synthethic division.

Answer to Problem 5QC

  $3x+2-\frac{20}{x+4}$

Explanation of Solution

Given Information:

Given expression is :

  $(3x^2+14x-12)÷(x+4)$

Concept Used :

Synthethic Division:

It is a method of dividing a polynomial with the binomial $x-c\text{ ; where c is a constant}$

• Steps to perform synthetic division:
• Set up the synthetic division.
• Bring down the leading coefficient to the bottom row.
• Multiply c by the value just written in the bottom row and write the result in the next column.
• Add the column just created in above step.
• Repeat until done.

Calculation:

  $\begin{array}{l}Given\\ (3x^2+14x-12)÷(x+4)\\ x-c=x-(-4)\\ So,\\ c=-4\\ Set\text{ up the synthetic division:}\\ \overline{)-4}\text{ 3 14 -12}\\ \downarrow \\ \overline{\text{ 3 }\hspace{.2em}|}\\ \text{Perform the synthetic division:}\\ \overline{)-4}\text{ 3 14 -12}\\ \downarrow \text{ -12 - 8}\\ \overline{\text{ 3 2 }\hspace{.2em}|}\overline{)-20}\\ \text{So, the result is :}\\ 3x+2-\frac{20}{x+4}\end{array}$