document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=59580>Question 59580</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could I please get some assistance with this?\r<BR>\n" );
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document.write( "Find the roots of the expression - factor the quadratic expression completely:<BR>\n" );
document.write( "6x^2 - 42x + 72\r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #40853 by </B><A HREF=/tutors/aboutme.mpl?userid=uma><B>uma(370)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=uma><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=40853\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 6x^2 - 42x + 72<BR>\n" );
document.write( " To factorise this, we need to find 2 numbers whose sum is -42 and whose product = 6*72 = 432\r<BR>\n" );
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document.write( "We find the numbers to be - 18 and - 24\r<BR>\n" );
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document.write( "Now 6x^2 - 42x + 72 <BR>\n" );
document.write( "= 6x^2 - 18x - 24x + 72  [splitting the middle term]<BR>\n" );
document.write( "= 6x(x - 3) - 24(x - 3)  [Removing the common factor]<BR>\n" );
document.write( "= (x - 3) (6x - 24)<BR>\n" );
document.write( "= (x - 3) (6) (x - 4)  [Removing the common factor]\r<BR>\n" );
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document.write( "So 6x^2 - 42x + 72  = 6(x - 3)(x - 4)\r<BR>\n" );
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document.write( "To find the roots, we equate this to zero.<BR>\n" );
document.write( "==>  6(x - 3)(x - 4) = 0<BR>\n" );
document.write( "==>  x - 3 = 0    or x - 4 = 0<BR>\n" );
document.write( "==>  x = 3  or  x = 4\r<BR>\n" );
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document.write( "So 3 and 4 are the roots of the given equation. </SPAN>\n" );
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