# Why It Matters: Factoring

## Why learn how to factor polynomials?

[latex]\begin{array}{l}x^2+6x-7=2x-4\\\,\,\,\,\,\,\,\,\underline{-2x}\,\,\,\,\,\,\,\,\,\,\,\,\,\underline{-2x}\,\,\,\,\,\,\\x^2+4x-7=-4\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\underline{+7}\,\,\,\,\,\,\,\,\,\underline{+7}\\x^2+4x=3\end{array}[/latex]

Ok, now what? We could try dividing all the terms by [latex]4[/latex] to isolate [latex]x[/latex], but we would still have [latex]x^2[/latex]. We will need different techniques than we use for solving linear equations to solve this equation. There are many methods for solving different kinds of polynomials using algebraic principles, but the truth is that most polynomials cannot be solved with the algebra we have used here.

At the end of this module, we will share some of the practical uses for solving polynomials that occur in our everyday lives. Polynomials are everywhere! They appear in electrical circuitry, mechanical systems, population ecology, roller coaster design, classrooms around the US, and even in the way Google's search engine ranks pages.

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**Provided by:**Lumen Learning**License:**CC BY: Attribution. - Why it Matters: Factoring.
**Provided by:**Lumen Learning**License:**CC BY: Attribution.