document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=755192>Question 755192</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what are the x-intercepts of h? \r<BR>\n" );
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document.write( "h(x)=(3x^4-54x^2+96x-45)/(2x^3-x^2-32x+16) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #459555 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=459555\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28x%29=%283x%5E4-54x%5E2%2B96x-45%29%2F%282x%5E3-x%5E2-32x%2B16%29=3%28x%5E4-18x%5E2%2B32x-15%29%2F%282x%5E3-x%5E2-32x%2B16%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The x-intercepts are the values of x that make h(x)=0.<BR>\n" );
document.write( "Those would be the values that make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4-18x%5E2%2B32x-15=0 ALIGN=MIDDLE  ALT=\"x%5E4-18x%5E2%2B32x-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "as long as they do not also make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E3-x%5E2-32x%2B16=0 ALIGN=MIDDLE  ALT=\"2x%5E3-x%5E2-32x%2B16=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If there are rational zeros for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4-18x%5E2%2B32x-15 ALIGN=MIDDLE  ALT=\"x%5E4-18x%5E2%2B32x-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >, they would be integers that are factors of 15.<BR>\n" );
document.write( "The possible zeros are -15, -5, -3, -1, 1, 3, 5, and 15.<BR>\n" );
document.write( "The only ones of those that could be a zero of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E3-x%5E2-32x%2B16 ALIGN=MIDDLE  ALT=\"2x%5E3-x%5E2-32x%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" > are -1 and 1, which are factors of 16, but neither is a zero of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E3-x%5E2-32x%2B16 ALIGN=MIDDLE  ALT=\"2x%5E3-x%5E2-32x%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " <BR>\n" );
document.write( "ZEROS OF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4-18x%5E2%2B32x-15 ALIGN=MIDDLE  ALT=\"x%5E4-18x%5E2%2B32x-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<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;\" > is obviously one of the zeros, since<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%5E4-18%2A1%5E2%2B32%2A1-15=1-18%2B32-15=0 ALIGN=MIDDLE  ALT=\"1%5E4-18%2A1%5E2%2B32%2A1-15=1-18%2B32-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4-18x%5E2%2B32x-15 ALIGN=MIDDLE  ALT=\"x%5E4-18x%5E2%2B32x-15\"   DISABLED_style= \"max-width:90%; height:auto;\" > divides exactly by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29 ALIGN=MIDDLE  ALT=\"%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > twice, and we find that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4-18x%5E2%2B32x-15=%28x-1%29%28x%5E3%2Bx%5E2-17x%2B15%29=%28x-1%29%28x-1%29%28x%5E2%2B2x-15%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x-15 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x-15\"   DISABLED_style= \"max-width:90%; height:auto;\" > is easy to factor as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x-15=%28x-3%29%28x%2B5%29 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x-15=%28x-3%29%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the full factorization of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4-18x%5E2%2B32x-15 ALIGN=MIDDLE  ALT=\"x%5E4-18x%5E2%2B32x-15\"   DISABLED_style= \"max-width:90%; height:auto;\" > is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4-18x%5E2%2B32x-15=%28x-1%29%5E2%28x-3%29%28x%2B5%29 ALIGN=MIDDLE  ALT=\"x%5E4-18x%5E2%2B32x-15=%28x-1%29%5E2%28x-3%29%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the x-intercepts of h(x), which are zeros of h(x) and of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4-18x%5E2%2B32x-15 ALIGN=MIDDLE  ALT=\"x%5E4-18x%5E2%2B32x-15\"   DISABLED_style= \"max-width:90%; height:auto;\" > are:<BR>\n" );
document.write( "<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;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=3%29 ALIGN=MIDDLE  ALT=\"highlight%28x=3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-5%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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