Q. 220 - Intermediate Algebra

Question

In the following exercises, factor completely.

$81x^2+169$

Step-by-Step Solution

Answer

The factored form of the given expression is $81x^2+169$.

Step 1. Given information.

The given expression is:
$81x^2+169$

Step 2. Determine the factored form.

The factor forms of 81 and 169 are:

$\begin{array}{rcl}81& =& 3\times 3\times 3\times 3\\ 169& =& 13\times 13\end{array}$

There is no common factor between $81x^2$ and 169.

The given expression can be written as:

$\begin{array}{rcl}81x^2+169& =& 9^2{x}^2+{\left(13\right)}^2 \\ & =& {\left(9x\right)}^2+{\left(13\right)}^2\end{array}$

It is clear that the expression cannot be factored. So, the factored form of the given expression is the expression itself.

Step 3. Conclusion.

The factored form of the given expression is $81x^2+169$.