document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=203311>Question 203311</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with factoring polynomials </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153406 by </B><A HREF=/tutors/aboutme.mpl?userid=PRMath><B>PRMath(133)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=PRMath><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=153406\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> That's a pretty broad question! :-)\r<BR>\n" );
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document.write( "Maybe you can send some examples of what confuses you.  When someone answers a specific question, it helps with the understanding.  In the meantime tho, I can give you the following info with regard to factoring polynomials.......\r<BR>\n" );
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document.write( "When you factor, you look for factors common to EVERY term in the equation.  For example:  \r<BR>\n" );
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document.write( "in this equation.... <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284y%5E2+-+8%29 ALIGN=MIDDLE  ALT=\"%284y%5E2+-+8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.... you have to ask yourself: \"What is common to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%5E2 ALIGN=MIDDLE  ALT=\"4y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > AND common to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8 ALIGN=MIDDLE  ALT=\"-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >also?\"\r<BR>\n" );
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document.write( "Do you see that the number 4 is common to both?  SO... what you do is sort of \"take out\" the 4 and put it in front of a parenthesis, to \"announce\" (so to speak) that you are dividing 4 from the entire equation.  \r<BR>\n" );
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document.write( "It's like this...   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28y%5E2+-+2%29 ALIGN=MIDDLE  ALT=\"4%28y%5E2+-+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The numbers in the parenthesis came when you made these divisions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284y%5E2%2F4%29 ALIGN=MIDDLE  ALT=\"%284y%5E2%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8%2F4 ALIGN=MIDDLE  ALT=\"-8%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Sometimes tho, you can divide out more than one common factor.  For example, in this problem............\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E4+%2B+20x%5E3 ALIGN=MIDDLE  ALT=\"5x%5E4+%2B+20x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .......... can you see that 5 is common to 5 and to 20?\r<BR>\n" );
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document.write( "BUT - can you also see that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is also common to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E4 ALIGN=MIDDLE  ALT=\"5x%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20x%5E3 ALIGN=MIDDLE  ALT=\"20x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >? \r<BR>\n" );
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document.write( "SO, let's \"take out\" or more specifically, let's divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E3 ALIGN=MIDDLE  ALT=\"5x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the whole equation, k?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E3%28x+%2B+4%29 ALIGN=MIDDLE  ALT=\"5x%5E3%28x+%2B+4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   \r<BR>\n" );
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document.write( "The above came when you made these divisions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E4%2F5x%5E3 ALIGN=MIDDLE  ALT=\"5x%5E4%2F5x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > along with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20x%5E3%2F5x%5E3 ALIGN=MIDDLE  ALT=\"20x%5E3%2F5x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "These are fairly simple factoring problems.  They can get more tricky but it's not clear at what level you get confused.  So again, I suggest you submit a problem you are struggling with, along with the steps you have taken to solve the problem.  Then your mistakes (if you make any) can be corrected.  \r<BR>\n" );
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document.write( "I hope this helps you. :-) </SPAN>\n" );
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