document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=920515>Question 920515</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help! Ive tried several times and can not get the correct answer.\r<BR>\n" );
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document.write( "Construct a polynomial with the stated properties. Reduce all fractions to lowest terms. <BR>\n" );
document.write( "Third-degree, with zeros of -2,-1, and 3,and passes through the point (2,10)\r<BR>\n" );
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document.write( "Answer p(x)=?? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #558437 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=558437\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the zeroes are -2, -1, and 3<BR>\n" );
document.write( "this means the factors are (x+2), (x+1), and (x-3)\r<BR>\n" );
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document.write( "(x+2) * (x+1) = x^2 + x + 2x + 2<BR>\n" );
document.write( "combine like terms to get x^2 + 3x + 2\r<BR>\n" );
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document.write( "x^2 + 3x + 2 * (x-3) = x^3 + 3x^2 + 2x - 3x^2 - 9x - 6<BR>\n" );
document.write( "combine like terms to get x^3 - 7x - 6\r<BR>\n" );
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document.write( "if the equation goes through the point (2,10), then f(2) must be equal to 10.\r<BR>\n" );
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document.write( "f(2), however, is equal to 2^3 - 7*2 - 6 which is equal to 8 - 14 - 6 which is equal to -12.\r<BR>\n" );
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document.write( "you can't just add 22 to it because that will change the roots.\r<BR>\n" );
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document.write( "you can, however, multiply it by a factor that will allow f(2) to be equal to 10 and not change the roots.\r<BR>\n" );
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document.write( "that factor is -5/6.\r<BR>\n" );
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document.write( "how did we find it?\r<BR>\n" );
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document.write( "we set a * (x^3 - 7x - 6) = y\r<BR>\n" );
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document.write( "replace y with 10 and x with 2 and you get:\r<BR>\n" );
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document.write( "a * (2^3 - 7*2 - 6) = 10\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "a * -12 = 10\r<BR>\n" );
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document.write( "divide both sides of the equation by -12 to get:\r<BR>\n" );
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document.write( "a = 10/-12.\r<BR>\n" );
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document.write( "simplify to get a = -5/6\r<BR>\n" );
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document.write( "your equation becomes:\r<BR>\n" );
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document.write( "-5/6 * (x^3 - 7x - 6) = y\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "-5/6 * x^3 + 35/6 * x + 30/6 = y\r<BR>\n" );
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document.write( "this simplifies to:\r<BR>\n" );
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document.write( "-5/6 * x^3 + 35/6 * x + 5 = y\r<BR>\n" );
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document.write( "f(2) now becomes:\r<BR>\n" );
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document.write( "f(2) = -5/6 * 2^3 + 35/6 * 2 + 5 which becomes:\r<BR>\n" );
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document.write( "f(2) = -5/6 * 8 + 70/6 + 5 which becomes:\r<BR>\n" );
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document.write( "f(2) = -40/6 + 70/6 + 5 which becomes:\r<BR>\n" );
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document.write( "f(2) = 30/6 + 5 which becomes:\r<BR>\n" );
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document.write( "f(2) = 5 + 5 which is equal to 10.\r<BR>\n" );
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document.write( "your equation now satisfies the requirements and has the same roots as it had before.<BR>\n" );
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