document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=115792>Question 115792</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0072934824/algebrahomeworkh>Algebra For college students</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Factor The Polynomial f(x). Then solve the equation f(x)=0<BR>\n" );
document.write( "1) F(x)= x^4-8x^3+17x^2+2X-24\r<BR>\n" );
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document.write( "2) -square root 7, -3i<BR>\n" );
document.write( "Find a polnomial function of lowest degree with rational coefficients that has the given numbers as some zeros. I have no idea where to start\r<BR>\n" );
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document.write( "3) f(x)=x^4-12x^2-64; -2i<BR>\n" );
document.write( "The polynomial function has the given zero, find the other zeros\r<BR>\n" );
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document.write( "I have no idea where to start some one point me in the right direction. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #84273 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=84273\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Factor The Polynomial f(x). Then solve the equation f(x)=0<BR>\n" );
document.write( "1) F(x)= x^4-8x^3+17x^2+2X-24<BR>\n" );
document.write( "Graphing I find x=-1 is a zero. x=2 is a zero, x=3 is a zero, x=4 is a zero.<BR>\n" );
document.write( "F(x) factors as (x+1)(x-2)(x-3)(x-4)<BR>\n" );
document.write( "----------------------\r<BR>\n" );
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document.write( "2) -square root 7, -3i<BR>\n" );
document.write( "Find a polnomial function of lowest degree with rational coefficients that has the given numbers as some zeros. I have no idea where to start<BR>\n" );
document.write( "Since the coefficients are rational 3i must also be a zero.<BR>\n" );
document.write( "Then: f(x) = (x-7)(x-3i)(x+3i)<BR>\n" );
document.write( "f(x) = (x-7)(x^2+9)<BR>\n" );
document.write( "f(x) = x^3-7x^2+9x-63<BR>\n" );
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document.write( "3) f(x)=x^4-12x^2-64; -2i<BR>\n" );
document.write( "The polynomial function has the given zero, find the other zeros<BR>\n" );
document.write( "Since the coefficients are rational 2i must also be a zero.<BR>\n" );
document.write( "So, f(x) = (x-2i)(x+2i)(?)<BR>\n" );
document.write( "f(x) = (x^2+4)(?)<BR>\n" );
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document.write( "Graph f(x) I find x=-4 is a zero, x=4 is a zero.<BR>\n" );
document.write( "Therefore: f(x) = (x^2+4)(x-4)(x+4)\r<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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