document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=431702>Question 431702</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the polynomial P(x) of lowest degree that has the zeros, 5,-5,1,-1.<BR>\n" );
document.write( "Answer: I know I have to set everything to 0. <BR>\n" );
document.write( "x-5=0<BR>\n" );
document.write( "x+5=0<BR>\n" );
document.write( "x-1=0<BR>\n" );
document.write( "x+1=0\r<BR>\n" );
document.write( "\n" );
document.write( "(x-5)(x+5)(x-1)(x+1)=0<BR>\n" );
document.write( "Now from there I don't know how to continue. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #299663 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=299663\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (x-5)(x+5)(x-1)(x+1)=0<BR>\n" );
document.write( "is mostly right. It should be:<BR>\n" );
document.write( "P(x) = (x-5)(x+5)(x-1)(x+1)<br><BR>\n" );
document.write( "All that is left is to multiply out the right side. I'd suggest mulitplying the first two factors and the last two factors first. For these we can use the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%28a-b%29+=+a%5E2-b%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%28a-b%29+=+a%5E2-b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > pattern to multiply quickly:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+%28x%5E2+-+5%5E2%29%28x%5E2+-+1%5E2%29 ALIGN=MIDDLE  ALT=\"P%28x%29+=+%28x%5E2+-+5%5E2%29%28x%5E2+-+1%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+%28x%5E2+-+25%29%28x%5E2+-+1%29 ALIGN=MIDDLE  ALT=\"P%28x%29+=+%28x%5E2+-+25%29%28x%5E2+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now just use FOIL to multiply the remaining factors. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );