document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=407811>Question 407811</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am struggling with this problem, Can someone please help? \r<BR>\n" );
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document.write( "Megan factored the expression 28x^2-25x+3 as (7x-3)(4x-1). But when Jacob applied the FOIL principle and mulitiplied out (7x-3)(4x-1), he got  28x^2-19x+3; thus, Megan's solution does not appear to check. Why is that? Please help Megan to understand this better. Explain your reasoning and correctly factor the original expression, if possible. If the expression is prime, so state.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #287381 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=287381\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28x%5E2-25x%2B3 ALIGN=MIDDLE  ALT=\"28x%5E2-25x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287x-3%29%284x-1%29 ALIGN=MIDDLE  ALT=\"%287x-3%29%284x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...let' multiply this\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287x%2A4x%2B7x%2A%28-1%29-3%2A4x+-3%2A%28-1%29%29 ALIGN=MIDDLE  ALT=\"%287x%2A4x%2B7x%2A%28-1%29-3%2A4x+-3%2A%28-1%29%29\"   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=28x%5E2+-7x+-12x+%2B3 ALIGN=MIDDLE  ALT=\"28x%5E2+-7x+-12x+%2B3\"   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=28x%5E2+-19x+%2B3 ALIGN=MIDDLE  ALT=\"28x%5E2+-19x+%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >...........Jacob was right\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28x%5E2-25x%2B3 ALIGN=MIDDLE  ALT=\"28x%5E2-25x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >....here Megan needed to replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-25x ALIGN=MIDDLE  ALT=\"-25x\"   DISABLED_style= \"max-width:90%; height:auto;\" > with sum or difference of two numbers in order to group terms (she needed four terms in this expression)\r<BR>\n" );
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document.write( "she took <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7x+-12x ALIGN=MIDDLE  ALT=\"-7x+-12x\"   DISABLED_style= \"max-width:90%; height:auto;\" > which makes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-19x ALIGN=MIDDLE  ALT=\"-19x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "she needed to replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-25x ALIGN=MIDDLE  ALT=\"-25x\"   DISABLED_style= \"max-width:90%; height:auto;\" > with a pair of numbers that add to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-25 ALIGN=MIDDLE  ALT=\"-25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " first of all she needed to multiply the leading coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28 ALIGN=MIDDLE  ALT=\"28\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the last term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,-she would have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=84 ALIGN=MIDDLE  ALT=\"84\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "second of all she needed to list all of the possible factors of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=84 ALIGN=MIDDLE  ALT=\"84\"   DISABLED_style= \"max-width:90%; height:auto;\" > and next\r<BR>\n" );
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document.write( "these factors pair up to multiply to 84 and see which of these pairs add to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-25 ALIGN=MIDDLE  ALT=\"-25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "1*84=84\r<BR>\n" );
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document.write( "2*42=84\r<BR>\n" );
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document.write( "3*28=84\r<BR>\n" );
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document.write( "4*21=84\r<BR>\n" );
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document.write( "6*14=84\r<BR>\n" );
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document.write( "7*12=84\r<BR>\n" );
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document.write( "(-1)*(-84)=84\r<BR>\n" );
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document.write( "(-2)*(-42)=84\r<BR>\n" );
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document.write( "(-3)*(-28)=84\r<BR>\n" );
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document.write( "(-4)*(-21)=84\r<BR>\n" );
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document.write( "(-6)*(-14)=84\r<BR>\n" );
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document.write( "(-7)*(-12)=84\r<BR>\n" );
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document.write( "We can see from the table that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-21 ALIGN=MIDDLE  ALT=\"-21\"   DISABLED_style= \"max-width:90%; height:auto;\" > add to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-25 ALIGN=MIDDLE  ALT=\"-25\"   DISABLED_style= \"max-width:90%; height:auto;\" >; so, she needed them to use\r<BR>\n" );
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document.write( "let's try it:\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28x%5E2-25x%2B3 ALIGN=MIDDLE  ALT=\"28x%5E2-25x%2B3\"   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=28x%5E2+-4x+-21x%2B3 ALIGN=MIDDLE  ALT=\"28x%5E2+-4x+-21x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >...group terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2828x%5E2+-4x%29%2B%28+-21x%2B3%29 ALIGN=MIDDLE  ALT=\"%2828x%5E2+-4x%29%2B%28+-21x%2B3%29\"   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=4x%287x+-1%29-3%287x-1%29 ALIGN=MIDDLE  ALT=\"4x%287x+-1%29-3%287x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287x-1%29 ALIGN=MIDDLE  ALT=\"%287x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a common term\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x-3%29%287x-1%29 ALIGN=MIDDLE  ALT=\"%284x-3%29%287x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......this would be her correct solution\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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