If the practical use of algebra and math broadly is to calculate an unknown answer then why is factoring polynomials still taught if it is merely a means to rewrite data which one already has?

Question

If the practical use of algebra and math broadly is to calculate an unknown answer then why is factoring polynomials still taught if it is merely a means to rewrite data which one already has?

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Answer 1

I would actually assert that Algebra is altogether broadly described as a set of rules for manipulating expressions without altering the equality.

The fact that this manifests as an ability to convert 2x = 10 to x = 5 is only of importance when we assign physical representation to these equations otherwise there is no inherent significance that x = 5 has over 2x = 10.