document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=919925>Question 919925</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If f(x) = x^5 + Ax^2 - 2Ax + 2 and f(-1) = 4, find f(1). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #558075 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=558075\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equation is:\r<BR>\n" );
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document.write( "f(x) = x^5 + ax^2 - 2ax + 2\r<BR>\n" );
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document.write( "you also know that f(-1) = 4\r<BR>\n" );
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document.write( "replace x with -1 in your original equation and you get:\r<BR>\n" );
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document.write( "f(-1) = (-1)^5 + a(-1)^2 - 2a(-1) + 2 which becomes:\r<BR>\n" );
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document.write( "f(-1) = -1 + a + 2a + 2 which becomes:\r<BR>\n" );
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document.write( "f(-1) = 3a + 1\r<BR>\n" );
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document.write( "since f(-1) = 4, this means that:\r<BR>\n" );
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document.write( "3a + 1 = 4\r<BR>\n" );
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document.write( "subtract 1 from both sides of that equation to get:\r<BR>\n" );
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document.write( "3a = 3 which results in:\r<BR>\n" );
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document.write( "a = 1\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "to confirm, replace a in the original equation with 1.\r<BR>\n" );
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document.write( "the original equation becomes:\r<BR>\n" );
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document.write( "x^5 + x^2 - 2x + 2\r<BR>\n" );
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document.write( "f(-1) = (-1)^5 + (-1)^2 - 2(-1) + 2 which becomes:\r<BR>\n" );
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document.write( "f(-1) = -1 + 1 + 2 + 2 which becomes:\r<BR>\n" );
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document.write( "f(-1) = 4\r<BR>\n" );
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document.write( "this agrees with what you were given that f(-1) = 4, so the solution of a = 1 is good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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