document.write( "Question 92349: Find all positive values for k for which each of the following can be factored. \r
\n" ); document.write( "\n" ); document.write( "x^2 + x - k \n" ); document.write( "
Algebra.Com's Answer #67305 by Nate(3500)\"\" \"About 
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x^2 + x - k
\n" ); document.write( "That means you want factors of -k that sum to 1....
\n" ); document.write( "Plug:
\n" ); document.write( "~~~ No Negative Values Work
\n" ); document.write( "k = -2 ... nope
\n" ); document.write( "k = -1 ... nope
\n" ); document.write( "k = 0 ... yes
\n" ); document.write( "k = 1 ... nope
\n" ); document.write( "k = 2 ... yes
\n" ); document.write( "k = 3 ... nope
\n" ); document.write( "k = 4 ... nope
\n" ); document.write( "k = 5 ... nope
\n" ); document.write( "k = 6 ... yes
\n" ); document.write( "k = 7 ... nope
\n" ); document.write( "k = 8 ... nope
\n" ); document.write( "k = 9 ... nope
\n" ); document.write( "k = 10 ... nope
\n" ); document.write( "k = 11 ... nope
\n" ); document.write( "k = 12 ... yes
\n" ); document.write( "~~~Skip a Few
\n" ); document.write( "k = 20 ... yes
\n" ); document.write( "Works: 2,6,12,20 ....
\n" ); document.write( "+2,+4,+6,+8,+10 ....
\n" ); document.write( "Arithmetic Sum:
\n" ); document.write( "S(k) = (k/2)(k1 + kx) ... where k1 is the first term and kx is the last term
\n" ); document.write( "S(k) = (k/2)(2 + k)
\n" ); document.write( "S(k) = k + k^2
\n" ); document.write( "First term: S(1) = 1 + 1^2 = 2
\n" ); document.write( "Second term: S(2) = 2 + 2^2 = 6
\n" ); document.write( "Kth term: S(k) = k + k^2 including zero \n" ); document.write( "
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