document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=392539>Question 392539</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor the following and list all the zeros (roots):\r<BR>\n" );
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document.write( "x^3+4x^2-4x-16 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #278610 by </B><A HREF=/tutors/aboutme.mpl?userid=haileytucki><B>haileytucki(390)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=haileytucki><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=haileytucki><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=278610\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x^(3)+4x^(2)-4x-16\r<BR>\n" );
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document.write( "If a polynomial function has integer coefficients, then every rational zero will have the form (p)/(q) where p is a factor of the constant and q is a factor of the leading coefficient.<BR>\n" );
document.write( "p=16_q=1\r<BR>\n" );
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document.write( "Find every combination of \(p)/(q).  These are the possible roots of the polynomial function.<BR>\n" );
document.write( "+-1,+-2,+-4,+-8,+-16\r<BR>\n" );
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document.write( "Substitute the possible roots one by one into the polynomial to find the actual roots.  Simplify to check if the value is 0, which means it is a root.<BR>\n" );
document.write( "(2)^(3)+4(2)^(2)-4(2)-16\r<BR>\n" );
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document.write( "Simplify the expression.  In this case, the expression is equal to 0 so x=2 is a root of the polynomial.<BR>\n" );
document.write( "0\r<BR>\n" );
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document.write( "Since 2 is a known root, divide the polynomial by (x-2) to find the quotient polynomial.  This polynomial can then be used to find the remaining roots.<BR>\n" );
document.write( "(x^(3)+4x^(2)-4x-16)/(x-2)\r<BR>\n" );
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document.write( "Complete the synthetic division of ((x^(3)+4x^(2)-4x-16))/((x-2)).<BR>\n" );
document.write( "2,1,4,-4,-16:1,1,2,12,16:1,1,6,8,0\r<BR>\n" );
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document.write( "Next, find the roots of the remaining polynomial.  The order of the polynomial has been reduced by 1.<BR>\n" );
document.write( "x^(2)+6x+8\r<BR>\n" );
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document.write( "Solve the equation to find any remaining roots.<BR>\n" );
document.write( "x=-4,-2\r<BR>\n" );
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document.write( "The polynomial can be written as a set of linear factors.<BR>\n" );
document.write( "(x-2)(x+4)(x+2)\r<BR>\n" );
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document.write( "These are the roots (i.e. zeros) of the polynomial x^(3)+4x^(2)-4x-16.<BR>\n" );
document.write( "x=2,-4,-2 </SPAN>\n" );
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