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 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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