document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=902623>Question 902623</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When a polynomial P(x) is divided by x + 3 , the remainder is 2. Which point must be on the <BR>\n" );
document.write( "graph of the corresponding function y = P(x). \r<BR>\n" );
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document.write( "Please show the steps and explain. I just can't figure this one out!\r<BR>\n" );
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document.write( "Your help is TRULY appreciated, thanks you thank you thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #547423 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=547423\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if f(a) = r, then the point (a,r) must be on the graph of the equation.\r<BR>\n" );
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document.write( "when you divide an equation by x - a, then this is the same as finding f(a) with r being the remainder of the division.\r<BR>\n" );
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document.write( "if you divide the polynomial by x+3, this is the same as finding f(-3) and the result of that will be the remainder of 2.\r<BR>\n" );
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document.write( "this means that the point (-3,2) must be on the graph.\r<BR>\n" );
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document.write( "an example will show you what i mean.\r<BR>\n" );
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document.write( "assume the equation is x^2 + x - 4\r<BR>\n" );
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document.write( "if you divide that equation by x+3, you will get 2 as a remainder.\r<BR>\n" );
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document.write( "if you evaluate f(x) = x^2 + x - 4 at f(-3), you will get (-3)^2 - 3 - 4 = 9 - 7 = 2\r<BR>\n" );
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document.write( "the point (-3,2) must be on the graph of the equation.\r<BR>\n" );
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document.write( "you can see if that's true by graphing x^2 + x - 4 and x = -3 and y = 2 and see if they intersect on the graph of that equation.\r<BR>\n" );
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document.write( "the graph looks like this:\r<BR>\n" );
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document.write( "the intersection of the vertical line at x = -3 and the horizontal line at y = 2 with the graph of the equation x^2 + x - 4 is at the point (-3,2).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C10%2C-10%2C10%2Cx%5E2+%2B+x+-+4%2C2%2C75%28x%2B3%29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C10%2C-10%2C10%2Cx%5E2+%2B+x+-+4%2C2%2C75%28x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "this is all part of the remainder theorem which you can read at the following link.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.purplemath.com/modules/remaindr.htm\" target = \"_blank\">http://www.purplemath.com/modules/remaindr.htm</a>\r<BR>\n" );
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