document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=907430>Question 907430</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The polynomial: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+-10%28x%2B5%29%5E2%28x%2B1%29%28x-4%29%5E3 ALIGN=MIDDLE  ALT=\"f%28x%29+=+-10%28x%2B5%29%5E2%28x%2B1%29%28x-4%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a. Then f is a polynomial of degree?\r<BR>\n" );
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document.write( "b. With the leading coefficient?\r<BR>\n" );
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document.write( "How would I solve the polynomial in order to get this information?<BR>\n" );
document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #550354 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=550354\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "You do not have anything that can be \"solved\".  In order to \"solve\" something you need some sort of relationship operator, such as an equals sign or an inequality sign.  I go to the trouble of saying this because precision of language is essential in mathematics.\r<BR>\n" );
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document.write( "Fortunately, you don't need to solve anything to find the information that is requested.  What you need to do is to expand the binomial expressions and collect like terms.  And even more fortunately, you don't even need to completely perform this operation.\r<BR>\n" );
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document.write( "Your factored form polynomial:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  f(x)\ =\ -10(x\ +\ 5)^2(x\ +\ 1)(x\ -\ 4)^3\">\r<BR>\n" );
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document.write( "If you expand the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x\ +\ 5)^2\"> binomial, you will get <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^2\"> plus some lower order terms forming a quadratic trinomial.  If you expand <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x\ -\ 4)^3\">, you get <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^3\"> plus some lower order terms forming a four-term cubic polynomial.  Then, multiplying a trinomial with an <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^2\"> high order term times a degree 1 binomial, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x\ +\ 1)\">, times a four term polynomial with a high order term of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^3\"> you will get a polynomial with a high order term of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^6\">.  Hence, the polynomial is degree 6.\r<BR>\n" );
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document.write( "Then, you multiply through by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -10\"> giving you a high-order term of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -10x^6\">, and by inspection, the lead coefficient is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -10\">.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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