document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=100274>Question 100274</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If x+p is a factor of ax*+bx+3, show that p(b-ap)=3. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #73019 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=73019\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Before I start, if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2B3=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2B3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx=-3 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So keep this fact in mind\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28b-ap%29 ALIGN=MIDDLE  ALT=\"p%28b-ap%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the left side of the second expression\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=bp-ap%5E2 ALIGN=MIDDLE  ALT=\"bp-ap%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "Since we're assuming x+p is a factor, this means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-p ALIGN=MIDDLE  ALT=\"x=-p\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=-x ALIGN=MIDDLE  ALT=\"p=-x\"   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=b%28-x%29-a%28-x%29%5E2 ALIGN=MIDDLE  ALT=\"b%28-x%29-a%28-x%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=-x ALIGN=MIDDLE  ALT=\"p=-x\"   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=-bx-ax%5E2 ALIGN=MIDDLE  ALT=\"-bx-ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-ax%5E2-bx ALIGN=MIDDLE  ALT=\"-ax%5E2-bx\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28ax%5E2%2Bbx%29 ALIGN=MIDDLE  ALT=\"-%28ax%5E2%2Bbx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out a negative 1\r<BR>\n" );
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document.write( "Remember <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx=-3 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so  let's substitute that in\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28-3%29 ALIGN=MIDDLE  ALT=\"-%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx\"   DISABLED_style= \"max-width:90%; height:auto;\" > with -3\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -3 to get 3\r<BR>\n" );
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document.write( "So we've algebraically manipulated <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28b-ap%29 ALIGN=MIDDLE  ALT=\"p%28b-ap%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 3. So we've just shown that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28b-ap%29 ALIGN=MIDDLE  ALT=\"p%28b-ap%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equal to 3\r<BR>\n" );
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document.write( "So that means we've proven that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28b-ap%29=3 ALIGN=MIDDLE  ALT=\"p%28b-ap%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is true. <BR>\n" );
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