document.write( "Question 1164615: Find all positive values of k so that the trinomial can be factored. Show the factorization for each value of k you find.\r
\n" ); document.write( "\n" ); document.write( "3x^2 + kx - 15 \n" ); document.write( "
Algebra.Com's Answer #789038 by greenestamps(13200)\"\" \"About 
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\n" ); document.write( "The factorization is of the form

\n" ); document.write( "(ax+b)(cx+d)

\n" ); document.write( "We know

\n" ); document.write( "(1) ac=3
\n" ); document.write( "(2) bd=-15

\n" ); document.write( "We can assume a and c are positive, because having both negative will not lead to different factorizations.

\n" ); document.write( "List all the possible factorizations that satisfy (1) and (2) and identify the ones that have k>0.

\n" ); document.write( "(3x+1)(x-15) k = -44
\n" ); document.write( "(3x-1)(x+15) k = 44
\n" ); document.write( "(3x+3)(x-5) k = -12
\n" ); document.write( "(3x-3)(x+5) k = 12
\n" ); document.write( "(3x+5)(x-3) k = -4
\n" ); document.write( "(3x-5)(x+3) k = 4
\n" ); document.write( "(3x+15)(x-1) k = 12
\n" ); document.write( "(3x-15)(x+1) k = -12

\n" ); document.write( "ANSWER: The possible positive values of k for which the trinomial can be factored are 4, 12, and 44

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