MHB Factoring x^2 + 64: Is it Possible?

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The expression x^2 + 64 cannot be factored over the integers as it is considered irreducible. Participants in the discussion agree on this point, confirming that no integer factors exist for the expression. The consensus emphasizes the inability to simplify x^2 + 64 into a product of linear factors. This reinforces the understanding of irreducibility in polynomial expressions. Therefore, x^2 + 64 remains unfactorable in the realm of integer coefficients.
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Factor x^2 + 64.

I say it cannot be factored because the expression is irreducible over integers.

Right?
 
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RTCNTC said:
Factor x^2 + 64.

I say it cannot be factored because the expression is irreducible over integers.

Right?
Yeppers!

-Dan
 
Cool.
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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