document.write( "Question 36336: factor the quadratic expression completely, and find the roots of the expression.\r
\n" ); document.write( "\n" ); document.write( "6x^2 - 42x + 72 \n" ); document.write( "

Algebra.Com's Answer #22264 by Earlsdon(6294) $\"\"$ $\"About$

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Factor the expression:
\n" ); document.write( " $\"6x%5E2-42x%2B72\"$ First factor out a 6.
\n" ); document.write( " $\"6%28x%5E2-7%2B12%29\"$ Now factor the parentheses.
\n" ); document.write( " $\"6%28x-3%29%28x-4%29\"$ \r
\n" ); document.write( "\n" ); document.write( "To find the roots, you must have an \"equation\". So presumably, you mean this expression to be equal to zero.
\n" ); document.write( " $\"6x%5E2-42x%2B72+=+0\"$ Now we can find the roots. Factor as above.
\n" ); document.write( " $\"6%28x-3%29%28x-4%29+=+0\"$ Apply the zero products principle. 6 is not zero, so:
\n" ); document.write( " $\"%28x-3%29%28x-4%29+=+0\"$ Apply the zero products principle again.
\n" ); document.write( " $\"x-3+=+0\"$ and/or $\"x-4+=+0\"$
\n" ); document.write( "If $\"x-3+=+0\"$ then $\"x+=+3\"$
\n" ); document.write( "If $\"x-4+=+0\"$ then $\"x+=+4\"$ \r
\n" ); document.write( "\n" ); document.write( "The roots are:
\n" ); document.write( "x = 3
\n" ); document.write( "x = 4 \n" ); document.write( "

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