document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=6425>Question 6425</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you please explain what a linear factor is and how it works in this equation?<BR>\n" );
document.write( "2x^2 - x - 6\r<BR>\n" );
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document.write( "Thank you<BR>\n" );
document.write( " Michael G. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #3483 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=3483\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First of all, a linear factor is a factor whose highest power of the variable is 1.  In your example here because you have an x^2 as the highest power of x in the problem, it is said to be quadratic.  It is NOT linear.  Linear factors would be like: 3x + 2, x-4, -2x+3, etc.\r<BR>\n" );
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document.write( "Secondly, you have given an expression, NOT an equation.  An equation must have a left side, a right side, and an equal sign in it.  What you have given is an expression <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+-x+-6+ ALIGN=MIDDLE  ALT=\"2x%5E2+-x+-6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > which factors into this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+%2B+3%29%28x+-+2%29 ALIGN=MIDDLE  ALT=\"%282x+%2B+3%29%28x+-+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Therefore, each of these factors: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B3%29 ALIGN=MIDDLE  ALT=\"%282x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29 ALIGN=MIDDLE  ALT=\"%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are said to be \"linear factors.\"  How to factor these quadratic expressions into linear factors is another whole topic.  See some of my lesson plans on factoring either on the algebra.com website or my own website under Basic Algebra Chapter 2.  There are about three sections there on factoring.\r<BR>\n" );
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document.write( "R^2 at SCC </SPAN>\n" );
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