document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=669024>Question 669024</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is a quartic function with only the two real zeros given?\r<BR>\n" );
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document.write( "x = -4 and x = -1\r<BR>\n" );
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document.write( "A. y = x4 + 5x3 + 5x2 + 5x + 4	\r<BR>\n" );
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document.write( "B. y = x4 - 5x3 - 5x2 - 5x - 4	\r<BR>\n" );
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document.write( "C. y = -x4 + 5x3 + 5x2 + 5x + 4	\r<BR>\n" );
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document.write( "D. y = x4 + 5x3 + 5x2 + 5x - 5	 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #416030 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=416030\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> My solution mmay not be the expected way to go about it, but here it is.<BR>\n" );
document.write( "The four answers feature four different quartic polynomials.<BR>\n" );
document.write( "I'll call them:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%28x%29=+x%5E4+%2B+5x%5E3+%2B+5x%5E2+%2B+5x+%2B+4 ALIGN=MIDDLE  ALT=\"A%28x%29=+x%5E4+%2B+5x%5E3+%2B+5x%5E2+%2B+5x+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%28x%29=+x%5E4+-+5x%5E3+-+5x%5E2+-+5x+-+4 ALIGN=MIDDLE  ALT=\"B%28x%29=+x%5E4+-+5x%5E3+-+5x%5E2+-+5x+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28x%29=+-x%5E4+%2B+5x%5E3+%2B+5x%5E2+%2B+5x+%2B+4 ALIGN=MIDDLE  ALT=\"C%28x%29=+-x%5E4+%2B+5x%5E3+%2B+5x%5E2+%2B+5x+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%28x%29=+x%5E4+%2B+5x%5E3+%2B+5x%5E2+%2B+5x+-+5 ALIGN=MIDDLE  ALT=\"D%28x%29=+x%5E4+%2B+5x%5E3+%2B+5x%5E2+%2B+5x+-+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, their values are:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+%28-1%29+=+%28-1%29%5E4+%2B+5+%28-1%29%5E3+%2B+5+%28-1%29%5E2+%2B+5%28-1%29+%2B+4=1-5%2B5-5%2B4=0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%28-1%29=+%28-1%29%5E4+-+5+%28-1%29%5E3+-+5+%28-1%29%5E2+-+5%28-1%29+-+4=1%2B5-5%2B5-4=2 ALIGN=MIDDLE  ALT=\"B%28-1%29=+%28-1%29%5E4+-+5+%28-1%29%5E3+-+5+%28-1%29%5E2+-+5%28-1%29+-+4=1%2B5-5%2B5-4=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28x%29=+-%28-1%29%5E4+%2B+5+%28-1%29%5E3+%2B+5+%28-1%29%5E2+%2B+5%28-1%29+%2B+4=-1-5%2B5-5%2B4=-2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%28-1%29=+%28-1%29%5E4+%2B+5+%28-1%29%5E3+%2B+5+%28-1%29%5E2+%2B+5%28-1%29+-+5=1-5%2B5-5-5=-9 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Only <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28x%29+has+%7B%7B%7Bx=-1 ALIGN=MIDDLE  ALT=\"a%28x%29+has+%7B%7B%7Bx=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > for a zero.<BR>\n" );
document.write( "Does it have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4 ALIGN=MIDDLE  ALT=\"x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > for a zero?<BR>\n" );
document.write( "Does it have any other zeros?<BR>\n" );
document.write( "You would expect it to have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4 ALIGN=MIDDLE  ALT=\"x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > for a zero, and to have no other real zeros.<BR>\n" );
document.write( "I would chose answer A and be done.<BR>\n" );
document.write( "However, I can answer those two questions by factoring the polynomial.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%28x%29=+x%5E4+%2B+5x%5E3+%2B+5x%5E2+%2B+5x+%2B+4=%28x%5E4%2Bx%5E3%29+%2B+%284x%5E3%2B4x%5E2%29+%2B+%28x%5E2%2Bx%29+%2B+%284x%2B+4%29=%28x%2B1%29%28x%5E3%2B4x%5E2%2Bx%2B4%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%28x%29=%28x%2B1%29%28x%5E3%2B4x%5E2%2Bx%2B4%29=%28x%2B1%29%28%28x%5E3%2B4x%5E2%29%2B%28x%2B4%29%29=%28x%2B1%29%28%28x%5E2%2B1%29%28x%2B4%29%29=%28x%2B1%29%28x%2B4%29%28x%5E2%2B1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That is the complete factorization.<BR>\n" );
document.write( "Because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B1=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > has no real solutions, teh only zeros are the values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > that make the other two factors zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1=0 ALIGN=MIDDLE  ALT=\"x%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-1%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4=0 ALIGN=MIDDLE  ALT=\"x%2B4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-4%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );