mairie0708zl

2022-01-27

How do you simplify polynomials?

Amina Hall

You can simplify polynomials only if they have roots. You can think of polynomials as numbers, and of monomials of the form (x-a) as ' numbers. So, as you can write a composite numbers as product of 's, you can write a "composite" polynomial as product of monomials of the form (x-a), where a is a root of the polynomial. If the polynomial has no roots, it means that, in a certain sense, it is "'", and cannot thus be further simplified.
For example, ${x}^{2}+1$ has no (real) roots, so it cannot be simplified. On the other hand, ${x}^{2}-1$ has roots $±1$, so it can be simplified into (x+1)(x-1).
Finally, ${x}^{3}+x$ has a root for x=0. So, we can write as $x\left({x}^{2}+1\right)$, and for what we saw before, this expression is no longer simplifiable.

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