document.write( "Question 481263: factor the quadratic expression completely, and find the roots of the expression.\r
\n" ); document.write( "\n" ); document.write( "66x2 - 130x + 56\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #329561 by ccs2011(207) $\"\"$ $\"About$

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First factor out the common factor of 2
\n" ); document.write( " $\"2%2833x%5E2-65x%2B28%29=0\"$
\n" ); document.write( "Then find factors of (33*28) that add up to -65
\n" ); document.write( "The best way to do this is to break down the product into prime factors:
\n" ); document.write( "33*28 = 11*3*7*4
\n" ); document.write( "(11*3)+(7*4) = 33+28 = 61
\n" ); document.write( "(11*7)+(3*4)= 77+12 = 89
\n" ); document.write( "(11*4)+(3*7) = 44+21 = 65
\n" ); document.write( "This means we can split -65x into -44x -21x
\n" ); document.write( "Use factor by grouping
\n" ); document.write( " $\"2%2833x%5E2-44x-21x%2B28%29=0\"$
\n" ); document.write( " $\"2%2811x%283x-4%29-7%283x-4%29%29=0\"$
\n" ); document.write( " $\"2%283x-4%29%2811x-7%29=0\"$
\n" ); document.write( "To find the roots, first divide out the 2 **notice, it has no effect on the roots**
\n" ); document.write( "Then solve for each factored expression separately
\n" ); document.write( " $\"3x-4+=+0\"$
\n" ); document.write( " $\"3x=4\"$
\n" ); document.write( " $\"x+=+4%2F3\"$
\n" ); document.write( " $\"11x-7+=0\"$
\n" ); document.write( " $\"11x=7\"$
\n" ); document.write( " $\"x+=+7%2F11\"$
\n" ); document.write( "The two roots are x=4/3 and x=7/11 \n" ); document.write( "

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