How can factoring polynomials be used in real life?
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.
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.
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.
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