document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1157549>Question 1157549</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let p(x) = −x^4 + 3x^3 + 13x^2 − 15x.\r<BR>\n" );
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document.write( "(a) Find all zeros of p(x)\r<BR>\n" );
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document.write( "(b) Factor p(x) completely\r<BR>\n" );
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document.write( "(c) Sketch the graph of p(x) using a sign diagram </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #780423 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=780423\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> factor out a -x(x^3-3x^2-13x)+15)=0<BR>\n" );
document.write( "x=0 \r<BR>\n" );
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document.write( "synthetic division using -3\r<BR>\n" );
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document.write( "-3/ 1-----  -3 ------ -13 ----- 15<BR>\n" );
document.write( "shown to be 1 ---  -6 ----- 5. which is x2-6x+5\r<BR>\n" );
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document.write( "so -3 is a root, and the trinomial factors into (x-5)(x-1)\r<BR>\n" );
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document.write( "roots are -3, 0, 1, and 5<BR>\n" );
document.write( "factors are -x(x+3)(x-1)(x-5).\r<BR>\n" );
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document.write( " go back to -x^4+3x^3+13x^2-15x<BR>\n" );
document.write( "when x becomes very negative, < -3. so does the function<BR>\n" );
document.write( "-3 < x < 0 will be positive\r<BR>\n" );
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document.write( "0< X < 1 will be negative <BR>\n" );
document.write( "1 < x < 5 will be positive<BR>\n" );
document.write( "and for large + x >5 the function will be negative.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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