document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=976975>Question 976975</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello!\r<BR>\n" );
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document.write( "What are the rational zeros of this function? Please explain each step.\r<BR>\n" );
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document.write( "f(x) = x^3 – 21x – 20 \r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #598464 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=598464\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = x^3 – 21x – 20 <BR>\n" );
document.write( "I always like to try x = 1  or -1 as a first step<BR>\n" );
document.write( "f(-1) = -1 + 21 - 20 = 0, and<BR>\n" );
document.write( "(x + 1) is a factor of f(x)<BR>\n" );
document.write( "now we can apply synthetic division<BR>\n" );
document.write( "-1 | 1   0  -21  -20 |<BR>\n" );
document.write( "note: the 0 represents the x^2 coefficient since there is no x^2 in f(x)<BR>\n" );
document.write( "|       -1    1   20 |<BR>\n" );
document.write( "|    1  -1  -20    0 |<BR>\n" );
document.write( "the result is<BR>\n" );
document.write( "x^2 -x -20<BR>\n" );
document.write( "this polynomial can be factored<BR>\n" );
document.write( "(x-5)(x+4)<BR>\n" );
document.write( "therefore the complete factorization is<BR>\n" );
document.write( "(x+1)(x-5)(x+4) and<BR>\n" );
document.write( "our zeros are -1, 5, -4<BR>\n" );
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