document.write( "Question 432888: What is the greatest possible product that can be formed by two integers whose sum is -256? Show how u figured it out. \n" ); document.write( "

Algebra.Com's Answer #300061 by Alan3354(69443) $\"\"$ $\"About$

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p(x) = x*(-256 - x) = -x^2 - 256x
\n" ); document.write( "That's a parabola that opens down, so the vertex is a max.
\n" ); document.write( "The line of symmetry is x = -b/2a = 256/-2
\n" ); document.write( "x = -128
\n" ); document.write( "p(-128) = -16384 - 256*(-128)
\n" ); document.write( "= 16384
\n" ); document.write( "--------
\n" ); document.write( "The 2 integers are -128 & -128
\n" ); document.write( "---------------------
\n" ); document.write( "Another approach:
\n" ); document.write( "-256/2 = -128
\n" ); document.write( "Product of any 2 integers that add to -256 =
\n" ); document.write( "(-128 + x)*(-128 - x) where x = any integer from 0 to 128
\n" ); document.write( "Product = 16384 - x^2
\n" ); document.write( "For the product to be a max, x^2 has to be a minimum. Minimum = 0
\n" ); document.write( "--> -128 * -128
\n" ); document.write( " \n" ); document.write( "

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