document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=214081>Question 214081</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321578295/algebrahomeworkh>Intermediate Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> factor completely:\r<BR>\n" );
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document.write( "3x^2-13x+14 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #161690 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><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/cgi-bin/show-face.mpl?user=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=161690\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Factor completely:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-13x%2B14=%283x-7%29%28x-2%29 ALIGN=MIDDLE  ALT=\"3x%5E2-13x%2B14=%283x-7%29%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 1.  We need to find two integers A and B that A*B=ac and A+B=b where \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > in order to be factorable and a=3, b=-13 and c=14\r<BR>\n" );
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document.write( "Step 2.  In the above example, then A*B=(3)(14)=42 and A+B=-13.  \r<BR>\n" );
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document.write( "Step 3.  After trial and error the numbers are A=-6 and B=-7\r<BR>\n" );
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document.write( "Step 4.  Using step 3, we can use grouping as follows \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-13x%2B14=3x%5E2-6x-7x%2B14 ALIGN=MIDDLE  ALT=\"3x%5E2-13x%2B14=3x%5E2-6x-7x%2B14\"   DISABLED_style= \"max-width:90%; height:auto;\" >  where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-13x=-6x-7x ALIGN=MIDDLE  ALT=\"-13x=-6x-7x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-13x%2B14=%283x%5E2-6x%29%2B%28-7x%2B14%29 ALIGN=MIDDLE  ALT=\"3x%5E2-13x%2B14=%283x%5E2-6x%29%2B%28-7x%2B14%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 5.  Factor out 3x in first group and -7 in second group\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-13x%2B14=3x%28x-2%29%2B%28-7%29%28x-2%29 ALIGN=MIDDLE  ALT=\"3x%5E2-13x%2B14=3x%28x-2%29%2B%28-7%29%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 6.  Factor out (x-2) since it is common in both groups.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-13x%2B14=%283x-7%29%28x-2%29 ALIGN=MIDDLE  ALT=\"3x%5E2-13x%2B14=%283x-7%29%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  ANSWER\r<BR>\n" );
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document.write( "We can use the FOIL method to verify\r<BR>\n" );
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document.write( "I hope the above steps were helpful. \r<BR>\n" );
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document.write( "For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r<BR>\n" );
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document.write( "And good luck in your studies!\r<BR>\n" );
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document.write( "Respectfully,<BR>\n" );
document.write( "Dr J\r<BR>\n" );
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document.write( " </SPAN>\n" );
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