Chapter 7, Problem 6QC

To determine

To Simplify :

The given expression by using synthethic division.

Answer to Problem 6QC

  $2x^2+5x-6$

Explanation of Solution

Given Information:

Given expression is :

  $(2x^3-7x^2-36x+36)÷(x-6)$

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:

  $\begin{array}{l}Given\\ (2x^3-7x^2-36x+36)÷(x-6)\\ x-c=x-6\\ So,\\ c=6\\ Set\text{ up the synthetic division:}\\ \overline{)6}\text{ 2 -7 -36 36 }\\ \downarrow \\ \overline{\text{ 2 }\hspace{.2em}|}\\ \\ \text{Perform the synthetic division:}\\ \overline{)6}\text{ 2 -7 -36 36 }\\ \downarrow \text{ 12 30 -36}\\ \overline{\text{ 2 5 -6 }\hspace{.2em}|}\overline{)\text{ 0 }}\\ \text{So, the result is :}\\ 2x^2+5x-6\end{array}$