# How Is the Factoring of Polynomials Used in Everyday Life?

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The factoring of a polynomial refers to finding polynomials of lower order (highest exponent is lower) that, multiplied together, produce the polynomial being factored. For example, x^2 - 1 can be factored into x - 1 and x + 1. When these factors are multiplied, the -1x and +1x cancel out, leaving x^2 and 1.

## Of Limited Power

Unfortunately, factoring is not a powerful tool, which limits its use in everyday life and technical fields. Polynomials are heavily rigged in grade school so that they can be factored. In everyday life, polynomials are not as friendly and require more sophisticated tools of analysis. A polynomial as simple as x^2 + 1 isn't factorable without using complex numbers--i.e., numbers that include i = √(-1). Polynomials of order as low as 3 can be prohibitively difficult to factor. For example, x^3 - y^3 factors to (x - y)(x^2 + xy + y^2), but it factors no further without resorting to complex numbers.

## High School Science

Second-order polynomials--e.g., x^2 + 5x + 4--are regularly factored in algebra classes, around eighth or ninth grade. The purpose of factoring such functions is to then be able to solve equations of polynomials. For example, the solution to x^2 + 5x + 4 = 0 are the roots of x^2 + 5x + 4, namely, -1 and -4. Being able to find the roots of such polynomials is basic to solving problems in science classes in the following 2 to 3 years. Second-order formulas come up regularly in such classes, e.g., in projectile problems and acid-base equilibrium calculations.