document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=472101>Question 472101</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all zeros of the function and write the polynomial as a product of linear 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+=+x%5E4+%2B+6x%5E3+%2B+17x%5E2+%2B+54x+%2B+72++ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+x%5E4+%2B+6x%5E3+%2B+17x%5E2+%2B+54x+%2B+72++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "a. f(x) = (x - 4)(x + 2)(x - 3)(x + 3)  <BR>\n" );
document.write( "b. f(x) = (x + 4)(x + 2)(x - 3i)(x + 3i)  <BR>\n" );
document.write( "c. f(x) = (x - 1)(x - 8)(x - 3i)(x + 3i)  <BR>\n" );
document.write( "d. f(x) = (x - i(sqrt8))(x + i(sqrt8))(x - 3)(x +3)  <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #323802 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=323802\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find all zeros of the function and write the polynomial as a product of linear factors. <BR>\n" );
document.write( " f(x) = x^4 + 6x^3 + 17x^2 + 54x + 72<BR>\n" );
document.write( "a. f(x) = (x - 4)(x + 2)(x - 3)(x + 3) <BR>\n" );
document.write( "b. f(x) = (x + 4)(x + 2)(x - 3i)(x + 3i) <BR>\n" );
document.write( "c. f(x) = (x - 1)(x - 8)(x - 3i)(x + 3i) <BR>\n" );
document.write( "d. f(x) = (x - i(sqrt8))(x + i(sqrt8))(x - 3)(x +3)<BR>\n" );
document.write( "**<BR>\n" );
document.write( "We could use the Rational Roots Theorem to solve this one, but because there would be so many possible roots it would be a long and drawn out process. Hopefully, you are allowed to get the first two roots with a graphing calculator.  The graphing calculator shows that there are only two real rational roots, -2 and -4. I will show you how to find the other pair of imaginary roots.<BR>\n" );
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document.write( "Using synthetic division:<BR>\n" );
document.write( "-2).....1......6.......17......54........72<BR>\n" );
document.write( "................-2.......-8....-18......-72<BR>\n" );
document.write( "..........1......4.......9........36.........0 (-2 is a root)<BR>\n" );
document.write( "-4............-4.......0......-36<BR>\n" );
document.write( "..........1.....0........9.........0 (-4 is a root)<BR>\n" );
document.write( "f(x)=(x+2)(x+4)(x^2+9)<BR>\n" );
document.write( "x^2+9=0<BR>\n" );
document.write( "x^2=-9<BR>\n" );
document.write( "x=±&#8730;-9<BR>\n" );
document.write( "x=±3i<BR>\n" );
document.write( "f(x)=(x+2)(x+4)(x-3i)(x+3i)<BR>\n" );
document.write( "b. is the correct ans </SPAN>\n" );
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