document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117273>Question 117273</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor completely.	15x^2 – 21x + 6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85299 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=85299\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given to factor:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x%5E2-21x%2B2 ALIGN=MIDDLE  ALT=\"15x%5E2-21x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice first that each of the numbers in the three terms is divisible by 3, so the factor 3<BR>\n" );
document.write( "can be removed. This results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A%285x%5E2+-+7x+%2B+2%29 ALIGN=MIDDLE  ALT=\"3%2A%285x%5E2+-+7x+%2B+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So now let's concentrate on factoring the terms inside the parentheses. Note that  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2 ALIGN=MIDDLE  ALT=\"5x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > can<BR>\n" );
document.write( "only be factored into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2Ax ALIGN=MIDDLE  ALT=\"5x%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Therefore, if the trinomial in the parentheses can be <BR>\n" );
document.write( "factored, the factors will be of the form:<BR>\n" );
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document.write( "(5x ______)*(x _____)<BR>\n" );
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document.write( "Next notice that the last term in the trinomial is +2. It's factors can only be +2 and +1 or<BR>\n" );
document.write( "-2 and -1 because they must multiply together to give +2. Since the middle term of the <BR>\n" );
document.write( "trinomial is -7 we have to have minuses in the factors of the trinomial. So we assume that<BR>\n" );
document.write( "the factors of +2 that we will use are -2 and -1. This leaves two possibilities:<BR>\n" );
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document.write( "(5x - 1)*(x - 2)<BR>\n" );
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document.write( "or<BR>\n" );
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document.write( "(5x - 2)*(x - 1)<BR>\n" );
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document.write( "When you multiply out the (5x - 1)*(x - 2) you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2+-10x+-+x+%2B+2 ALIGN=MIDDLE  ALT=\"5x%5E2+-10x+-+x+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which reduces to <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2+-+11x+%2B+2 ALIGN=MIDDLE  ALT=\"5x%5E2+-+11x+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > so this combination does not work.<BR>\n" );
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document.write( "When you multiply out the (5x - 2)*(x - 1) you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2+-+5x+-+2x+%2B+2 ALIGN=MIDDLE  ALT=\"5x%5E2+-+5x+-+2x+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and this does reduce<BR>\n" );
document.write( "to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2+-7x+%2B2 ALIGN=MIDDLE  ALT=\"5x%5E2+-7x+%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, just as we need.<BR>\n" );
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document.write( "So now we can say that the given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x%5E2+-+21x%2B2 ALIGN=MIDDLE  ALT=\"15x%5E2+-+21x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "factors to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A%285x+-+2%29%2A%28x+-+1%29 ALIGN=MIDDLE  ALT=\"3%2A%285x+-+2%29%2A%28x+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "None of the expressions inside the parentheses can be factored, so this is the final answer.<BR>\n" );
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document.write( "Hope this helps to see how the given trinomial can be factored using a \"logical\" analysis and<BR>\n" );
document.write( "a little bit of trial.<BR>\n" );
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