document.write( "Question 445008: Find ALL values of k so 5x^2 + kx -6 will factor. Show all work please!
\n" ); document.write( "Thanks in advance \n" ); document.write( "

Algebra.Com's Answer #306697 by AnlytcPhil(1806) $\"\"$ $\"About$

You can put this solution on YOUR website!
Find ALL values of k so 5x^2 + kx -6 will factor. Show all work please!
\n" ); document.write( "Thanks in advance
\n" ); document.write( "

\r\n" );
document.write( "5x² + kx - 6 \r\n" );
document.write( "\r\n" );
document.write( "5 can only be factored as 5*1, so every possible\r\n" );
document.write( "factorization must be of this form:\r\n" );
document.write( "\r\n" );
document.write( "(5x    )(x    )\r\n" );
document.write( "\r\n" );
document.write( "Next all the ways to factor 6 are\r\n" );
document.write( "\r\n" );
document.write( "6*1, 3*2, 2*3 and 1*6\r\n" );
document.write( "\r\n" );
document.write( "so any possible factorization is in one of\r\n" );
document.write( "these four forms:\r\n" );
document.write( "\r\n" );
document.write( "(5x   6)(x   1)\r\n" );
document.write( "(5x   3)(x   2)\r\n" );
document.write( "(5x   2)(x   3)\r\n" );
document.write( "(5x   1)(x   6)\r\n" );
document.write( "\r\n" );
document.write( "Since the last term of 5x² + kx - 6 is negative \r\n" );
document.write( "the two signs must be opposite. So we have these\r\n" );
document.write( "8 possible factorizations, which we multiply out \r\n" );
document.write( "to find k in each case:\r\n" );
document.write( "\r\n" );
document.write( "(5x + 6)(x - 1)  =  5x² +   x - 6  so k =   1\r\n" );
document.write( "(5x + 3)(x - 2)  =  5x² -  7x - 6  so k =  -7  \r\n" );
document.write( "(5x + 2)(x - 3)  =  5x² - 13x - 6  so k = -13\r\n" );
document.write( "(5x + 1)(x - 6)  =  5x² - 29x - 6  so k = -29\r\n" );
document.write( "(5x - 6)(x + 1)  =  5x² -   x - 6  so k =  -1\r\n" );
document.write( "(5x - 3)(x + 2)  =  5x² +  7x - 6  so k =   7\r\n" );
document.write( "(5x - 2)(x + 3)  =  5x² + 13x - 6  so k =  13\r\n" );
document.write( "(5x - 1)(x + 6)  =  5x² + 29x - 6  so k =  29\r\n" );
document.write( "\r\n" );
document.write( "So all possible integer values of k are ±1, ±7, ±13, and ±29.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );