document.write( "Question 474274: Factor Completely\r
\n" ); document.write( "\n" ); document.write( "6x^3 - 16x^2 - 6x \n" ); document.write( "

Algebra.Com's Answer #325289 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+6x%5E3+-+16x%5E2+-+6x+\"$
\n" ); document.write( " $\"+2x%2A%283x%5E2+-+8x+-+3%29+\"$
\n" ); document.write( "Find the factors of the quadratic
\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"+a+=+3+\"$
\n" ); document.write( " $\"+b+=+-8+\"$
\n" ); document.write( " $\"+c+=+-3+\"$
\n" ); document.write( " $\"x+=+%28-%28-8%29+%2B-+sqrt%28+%28-8%29%5E2-4%2A3%2A%28-3%29+%29%29%2F%282%2A3%29+\"$
\n" ); document.write( " $\"x+=+%28+8+%2B-+sqrt%28+64+%2B+36+%29%29+%2F+6+\"$
\n" ); document.write( " $\"x+=+%28+8+%2B-+sqrt%28+100+%29%29+%2F+6+\"$
\n" ); document.write( " $\"x+=+%28+8+%2B+10%29+%2F+6+\"$
\n" ); document.write( " $\"+x+=+18%2F6+\"$
\n" ); document.write( "(1) $\"+x+=+3+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"x+=+%28+8+-+10%29+%2F+6+\"$
\n" ); document.write( " $\"+x+=+-2%2F6+\"$
\n" ); document.write( "(2) $\"+x+=+-1%2F3+\"$
\n" ); document.write( "Now rewrite (1) and (2) as:
\n" ); document.write( "(1) $\"+x+-+3+=+0+\"$
\n" ); document.write( "(2) $\"+x+%2B+1%2F3+=+0+\"$
\n" ); document.write( "(2) $\"+3x+%2B+1+=+0+\"$
\n" ); document.write( "so,
\n" ); document.write( " $\"+3x%5E2+-+8x+-+3++=+%28+x+-+3+%29%2A%28+3x+%2B+1+%29+\"$
\n" ); document.write( "The complete factorization is:
\n" ); document.write( " $\"+2x%2A%28+x+-+3+%29%2A%28+3x+%2B+1+%29+\"$
\n" ); document.write( "-----------
\n" ); document.write( "check:
\n" ); document.write( " $\"+2x%2A%283x%5E2+-+9x+%2B+x+-+3%29+\"$
\n" ); document.write( " $\"+2x%2A%283x%5E2+-+8x+-+3%29+\"$
\n" ); document.write( " $\"+6x%5E3+-+16x%5E2+-+6x+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );