document.write( "Question 389836: How can you determine an expression that is completely factored? \n" ); document.write( "
Algebra.Com's Answer #276391 by Alan3354(69443)\"\" \"About 
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How can you determine an expression that is completely factored?
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\n" ); document.write( "Never thought about that, but:
\n" ); document.write( "Completely factored = prime
\n" ); document.write( "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
\n" ); document.write( "If there is a common factor: 4x + 8 --> 4(x + 2)
\n" ); document.write( "1st order is obvious.
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\n" ); document.write( "For 2nd order:
\n" ); document.write( "f(x) = Ax^2 + Bx + C
\n" ); document.write( "If the function is a prime number for several values of x (I don't know how many are required) the expression is prime.
\n" ); document.write( "eg, f(x) = x^2 + 3x + 3
\n" ); document.write( "f(0) = 3
\n" ); document.write( "f(1) = 7
\n" ); document.write( "f(2) = 13
\n" ); document.write( "f(3) = 21 (not prime)
\n" ); document.write( "f(4) = 31
\n" ); document.write( "eg, f(x) = x^2 + 4x + 6
\n" ); document.write( "f(0) = 6 (not prime)
\n" ); document.write( "f(1) = 11
\n" ); document.write( "f(2) = 18 (not prime)
\n" ); document.write( "f(3) = 27 (np)
\n" ); document.write( "f(5) = 51 (np)
\n" ); document.write( "f(7) = 73
\n" ); document.write( "f(9) = 123 (np)
\n" ); document.write( "f(11) = 171 (np)
\n" ); document.write( "f(13) = 227
\n" ); document.write( "Finding only one (1) prime value is sufficient to determine that a binomial is prime.
\n" ); document.write( "This is sufficient for any expression, regardless of exponents.
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