document.write( "Question 580002: factor completely\r
\n" ); document.write( "\n" ); document.write( "x^6 - 14x^4 + 49x^2\r
\n" ); document.write( "\n" ); document.write( "i have no clue where to even begin please help \n" ); document.write( "

Algebra.Com's Answer #371125 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
I can factor out an $\"+x%5E2+\"$
\n" ); document.write( " $\"+x%5E2%2A%28+x%5E4+-+14x%5E2+%2B+49+%29+\"$
\n" ); document.write( "Now I can make the substitution $\"+x%5E2+=+z+\"$
\n" ); document.write( " $\"+z%2A%28+z%5E2+-+14z+%2B+49+%29+\"$
\n" ); document.write( "To factor this completely, I
\n" ); document.write( "complete the square on the 2nd factor:
\n" ); document.write( " $\"+z%5E2+-+14z+%2B+%2814%2F2%29%5E2+=+-49+%2B+%2814%2F2%29%5E2+\"$
\n" ); document.write( " $\"+z%5E2+-+14z+%2B+49+=+-49+%2B+49+\"$
\n" ); document.write( " $\"+%28+z+-+7+%29%5E2+=+0+\"$
\n" ); document.write( " $\"+z+-+7+=+0+\"$
\n" ); document.write( "This is called a double root, so the factorization is:
\n" ); document.write( " $\"+z%2A%28+z+-+7+%29%5E2+\"$
\n" ); document.write( "Now substitute $\"+z+=+x%5E2+\"$
\n" ); document.write( " $\"+x%5E2%2A%28+x%5E2+-+7+%29%5E2+\"$
\n" ); document.write( "This can be factored 1 more step:
\n" ); document.write( " $\"+x%5E2%2A%28+x+%2B+sqrt%287%29+%29%5E2%28+x+-+sqrt%287%29+%29%5E2+\"$
\n" ); document.write( "Hope I got it
\n" ); document.write( "Here's a plot of the equation:
\n" ); document.write( " $\"+graph%28+500%2C+500%2C+-4%2C+4%2C+-2%2C+16%2C+x%5E6+-+14x%5E4+%2B+49x%5E2+%29+\"$ \r
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