document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=489000>Question 489000</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Andrew factored the expression28x^2-42x^2+35x as 7x(4x^2+6x-5) . But when Melissa applied the distributive law and multiplied out7x(4x^2+6x-5) , she got28x^3+24x^2-23x ; thus, Andrew’s solution does not appear to check. Why is that? Please help Andrew 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 #333501 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=333501\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Andrew factored the expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28x%5E2-42x%5E2%2B35x ALIGN=MIDDLE  ALT=\"28x%5E2-42x%5E2%2B35x\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%284x%5E2%2B6x-5%29 ALIGN=MIDDLE  ALT=\"7x%284x%5E2%2B6x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . \r<BR>\n" );
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document.write( "But when Melissa applied the distributive law and multiplied out7x(4x^2+6x-5) , she got\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28x%5E3%2B24x%5E2-23x+ ALIGN=MIDDLE  ALT=\"28x%5E3%2B24x%5E2-23x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >; \r<BR>\n" );
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document.write( "let's check first Melisa's result:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%284x%5E2%2B6x-5%29 ALIGN=MIDDLE  ALT=\"7x%284x%5E2%2B6x-5%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=7x%2A4x%5E2%2B6x%2A7x-5%2A7x ALIGN=MIDDLE  ALT=\"7x%2A4x%5E2%2B6x%2A7x-5%2A7x\"   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=28%5E3%2B42x%5E2-35x ALIGN=MIDDLE  ALT=\"28%5E3%2B42x%5E2-35x\"   DISABLED_style= \"max-width:90%; height:auto;\" >....she made these mistakes when multiplied <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%284x%5E2%2B6x-5%29 ALIGN=MIDDLE  ALT=\"7x%284x%5E2%2B6x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >: for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2A7x-5%2A7x ALIGN=MIDDLE  ALT=\"6x%2A7x-5%2A7x\"   DISABLED_style= \"max-width:90%; height:auto;\" > she got <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24x%5E2-23x+ ALIGN=MIDDLE  ALT=\"24x%5E2-23x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >...(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A7=42 ALIGN=MIDDLE  ALT=\"6%2A7=42\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2A7=-35 ALIGN=MIDDLE  ALT=\"-5%2A7=-35\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "but, Andrew’s solution does not check either because he made mistake with a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=minus ALIGN=MIDDLE  ALT=\"minus\"   DISABLED_style= \"max-width:90%; height:auto;\" > sign \r<BR>\n" );
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document.write( "in expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28x%5E2-42x%5E2%2B35x ALIGN=MIDDLE  ALT=\"28x%5E2-42x%5E2%2B35x\"   DISABLED_style= \"max-width:90%; height:auto;\" > coefficients are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28 ALIGN=MIDDLE  ALT=\"28\"   DISABLED_style= \"max-width:90%; height:auto;\" > (positive), <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-42 ALIGN=MIDDLE  ALT=\"-42\"   DISABLED_style= \"max-width:90%; height:auto;\" > (negative), and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35 ALIGN=MIDDLE  ALT=\"35\"   DISABLED_style= \"max-width:90%; height:auto;\" > (positive)\r<BR>\n" );
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document.write( "so, instead of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%284x%5E2%2B6x-5%29 ALIGN=MIDDLE  ALT=\"7x%284x%5E2%2B6x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, he should have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%284x%5E2-6x%2B5%29 ALIGN=MIDDLE  ALT=\"7x%284x%5E2-6x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I hope Andrew will understand this better now. So, be careful with the signs and do a quick check that the distributive law takes you back to the expression you started with.\r<BR>\n" );
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document.write( "correctly factored original expression: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%284x%5E2-6x%2B5%29 ALIGN=MIDDLE  ALT=\"7x%284x%5E2-6x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " If the expression is prime: It isn't prime if it have factors besides 1 and itself.  </SPAN>\n" );
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