SOLUTION: How can you determine an expression that is completely factored?

Question 389836: How can you determine an expression that is completely factored?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
How can you determine an expression that is completely factored?
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Never thought about that, but:
Completely factored = prime
If it's 1st order and there's no common factor for the 2 coefficients, it's prime. eg, x + 2, 2x + 3, 3x - 5, etc
If there is a common factor: 4x + 8 --> 4(x + 2)
1st order is obvious.
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For 2nd order:
f(x) = Ax^2 + Bx + C
If the function is a prime number for several values of x (I don't know how many are required) the expression is prime.
eg, f(x) = x^2 + 3x + 3
f(0) = 3
f(1) = 7
f(2) = 13
f(3) = 21 (not prime)
f(4) = 31
eg, f(x) = x^2 + 4x + 6
f(0) = 6 (not prime)
f(1) = 11
f(2) = 18 (not prime)
f(3) = 27 (np)
f(5) = 51 (np)
f(7) = 73
f(9) = 123 (np)
f(11) = 171 (np)
f(13) = 227
Finding only one (1) prime value is sufficient to determine that a binomial is prime.
This is sufficient for any expression, regardless of exponents.

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