document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1127820>Question 1127820</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Someone please help me with this question.\r<BR>\n" );
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document.write( "What are the factors of the polynomial function?\r<BR>\n" );
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document.write( "Use the rational root theorem to determine the factors.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29=+2x%5E3+%2B+x%5E2+-+8x+-+4++ ALIGN=MIDDLE  ALT=\"+f%28x%29=+2x%5E3+%2B+x%5E2+-+8x+-+4++\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Select EACH correct answer.\r<BR>\n" );
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document.write( "A. (2x + 1)\r<BR>\n" );
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document.write( "B. (2x - 1)\r<BR>\n" );
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document.write( "C. (x + 2)\r<BR>\n" );
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document.write( "D. (x - 2)\r<BR>\n" );
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document.write( "E. (x - 1)\r<BR>\n" );
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document.write( "F. (x + 1)\r<BR>\n" );
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document.write( "G. (x - 4)\r<BR>\n" );
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document.write( "H. (x + 4) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #744278 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=744278\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The rational roots theorem says that the possible rational roots for a polynomial are +/-(p/q), where p is a factor of the constant term and q is a factor of the leading coefficient.  For this polynomial then, the possible roots are<br><BR>\n" );
document.write( "+/- {1, 2, 4, 1/2}<br><BR>\n" );
document.write( "When you find one root, you can divide the polynomial by the corresponding linear factor to obtain a quadratic polynomial; you can then find the other two roots by factoring the quadratic or using the quadratic formula.<br><BR>\n" );
document.write( "So you only need to find one root using the rational roots theorem.  Which ones should you try first?<br><BR>\n" );
document.write( "1 and -1 are always the easiest to test, simply by evaluating the polynomial for those values.  In this example, neither 1 nor -1 is a root.<br><BR>\n" );
document.write( "For the other possible rational roots, some students will prefer evaluating the polynomial; other students will find synthetic division easier.  Try the smaller integers (positive and negative) first.  And hope that you find a root before you need to test the fractions.<br><BR>\n" );
document.write( "In this example, the polynomial evaluated at x=2 is 0, so 2 is a root.  Dividing the polynomial by the linear factor (x-2) using synthetic division shows the remaining polynomial to be 2x^2+5x+2.  That is easily factored to finish the factorization of the polynomial. </SPAN>\n" );
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