document.write( "Question 224747: Determine the x-intercepts of $\"f%28x%29=%28x%5E2-6x%29%5E2-2%28x%5E2-6x%29-35\"$ \n" ); document.write( "

Algebra.Com's Answer #167872 by LtAurora(115) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( " $\"f%28x%29=%28x%5E2-6x%29%5E2-2%28x%5E2-6x%29-35\"$
\n" ); document.write( "Substitute out the messy bit:
\n" ); document.write( " $\"u=%28x%5E2-6x%29\"$
\n" ); document.write( "This gives a more reasonable looking equation:
\n" ); document.write( " $\"f%28x%29=u%5E2-2u-35\"$
\n" ); document.write( "Which can be factored as:
\n" ); document.write( " $\"f%28x%29=%28u%2B5%29%28u-7%29\"$
\n" ); document.write( "Then, substitute $\"x\"$ back in:
\n" ); document.write( " $\"f%28x%29=%28%28x%5E2-6x%29%2B5%29%28%28x%5E2-6x%29-7%29\"$
\n" ); document.write( "This yields
\n" ); document.write( " $\"f%28x%29=%28x%5E2-6x%2B5%29%28x%5E2-6x-7%29\"$
\n" ); document.write( "Which can factor down to:
\n" ); document.write( " $\"f%28x%29=%28x-6%29%28x-1%29%28x-7%29%28x%2B1%29\"$
\n" ); document.write( "Thus the x-intercepts are:
\n" ); document.write( "x=6,1,7,-1\r
\n" ); document.write( "\n" ); document.write( "This type problem could also be done with synthetic division, but this particular one factors without too much difficulty. \n" ); document.write( "

\n" );