Chapter 7, Problem 7QC

To determine

To Simplify :

The given expression by using synthethic division.

Answer to Problem 7QC

  $3x^3-4x^2+5x-3+\frac{6}{x-3}$

Explanation of Solution

Given Information:

Given expression is :

  $(3x^4-13x^3+17x^2-18x+15)÷(x-3)$

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:

  $\begin{array}{l}Given\\ (3x^4-13x^3+17x^2-18x+15)÷(x-3)\\ x-c=x-3\\ So,\\ c=3\\ Set\text{ up the synthetic division:}\\ \overline{)3}\text{ 3 -13 17 -18 15 }\\ \downarrow \\ \overline{\text{ 3 }\hspace{.2em}|}\\ \\ \text{Perform the synthetic division:}\\ \overline{)3}\text{ 3 -13 17 -18 15 }\\ \downarrow \text{ 9 -12 15 -9}\\ \overline{\text{ 3 -4 5 -3 }\hspace{.2em}|}\overline{)\text{ 6 }}\\ \text{So, the result is :}\\ 3x^3-4x^2+5x-3+\frac{6}{x-3}\end{array}$