document.write( "Question 978038: Find the value of k for which a-3b is a factor of a⁴-7a²b²+kb⁴. Hence for
\n" ); document.write( "this value of k , factorise a⁴-7a²b²+kb⁴ completely. \n" ); document.write( "

Algebra.Com's Answer #599554 by Edwin McCravy(20060) $\"\"$ $\"About$

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Find the value of k for which a-3b is a factor of a⁴-7a²b²+kb⁴ .
\n" ); document.write( "Hence for this value of k, factorise a⁴-7a²b²+kb⁴ completely.
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document.write( "Divide by long division, inserting zero terms for missing terms +0a³b and\r\n" );
document.write( "+0ab³:\r\n" );
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document.write( "         a³ +3a²b +2ab²+ 6b³   \r\n" );
document.write( "a-3b)a⁴+0a³b-7a²b²+0ab³+ kb⁴\r\n" );
document.write( "     a⁴-3a³b\r\n" );
document.write( "        3a³b-7a²b²\r\n" );
document.write( "        3a³b-9a²b²\r\n" );
document.write( "             2a²b²+0ab³\r\n" );
document.write( "             2a²b²-6ab³\r\n" );
document.write( "                   6ab³+ kb⁴\r\n" );
document.write( "                   6ab³-18b⁴\r\n" );
document.write( "                         kb⁴+18b⁴  <-- remainder\r\n" );
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document.write( "The remainder must = 0 so that a-3b \r\n" );
document.write( "will be a factor of a⁴-7a²b²+kb⁴.\r\n" );
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document.write( "kb⁴+18b⁴ = 0\r\n" );
document.write( "(k+18)b⁴ = 0\r\n" );
document.write( "k+18=0; b⁴=0\r\n" );
document.write( " k=-18;  b=0  \r\n" );
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document.write( "There is a trivial case for b=0 and k is any number, \r\n" );
document.write( "which we ignore.\r\n" );
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document.write( "So k = -18\r\n" );
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document.write( "a⁴-7a²b²-18b⁴\r\n" );
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document.write( "(a²+2b²)(a²-9b²)\r\n" );
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document.write( "(a²+2b²)(a-3b)(a+3b)\r\n" );
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document.write( "Edwin

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