document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=5468>Question 5468</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the specific difference between a \"term\" and a \"factor\"?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #2791 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=2791\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Terms are quantities that are added or subtracted together.  For example, in the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B+5y+-+7 ALIGN=MIDDLE  ALT=\"3x+%2B+5y+-+7\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x ALIGN=MIDDLE  ALT=\"3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a term, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y ALIGN=MIDDLE  ALT=\"5y\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a term, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7 ALIGN=MIDDLE  ALT=\"-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > is considered a term.  If you have terms that have the same variable(s)and the same powers, then they are \"like terms,\" and they can be combined.  For example <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B+5x ALIGN=MIDDLE  ALT=\"3x+%2B+5x\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be combined to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x ALIGN=MIDDLE  ALT=\"8x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, since both terms have the same variables raised to the same powers.  On the other hand, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B+5y ALIGN=MIDDLE  ALT=\"3x+%2B+5y\"   DISABLED_style= \"max-width:90%; height:auto;\" > are not like terms so they cannot be combined.  Also, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B+5x%5E2 ALIGN=MIDDLE  ALT=\"3x+%2B+5x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > are not like terms (different powers of x), so they also cannot be combined.\r<BR>\n" );
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document.write( "Factors are quantities that are multiplied together.  For example, in the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%28x-5%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the quantities <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29 ALIGN=MIDDLE  ALT=\"%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are said to be factors, since they are multiplied together.  Within the FACTOR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > you have two TERMS, that is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+ ALIGN=MIDDLE  ALT=\"x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  They are called terms because they are added (or subtracted) together.\r<BR>\n" );
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document.write( "That is a very important question to ask.  I probably need to write a lesson plan for this, but for now at least, I have a section on this topic in my book and on my website (double click on my tutor name) under Basic Algebra Section 1.06.  Let me know if you are interested in seeing more, and if you need help finding it.\r<BR>\n" );
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document.write( "R^2 at SCC </SPAN>\n" );
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