document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170859>Question 1170859</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the values of  A,B,C if (x-1),(x+2) and (x-2) are factor of<BR>\n" );
document.write( "2Ax^4-Bx^3-Cx-16 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #795736 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=795736\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "We have three factors: (x-1),(x+2) and (x-2)<BR>\n" );
document.write( "However, we have a quartic polynomial, since the degree (largest exponent) is 4\r<BR>\n" );
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document.write( "So we need a fourth factor. Let's call that x-p, for some real number p.\r<BR>\n" );
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document.write( "Let's expand out the following<BR>\n" );
document.write( "(x-1)(x+2)(x-2)(x-p)\r<BR>\n" );
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document.write( "(x+2)(x-2)(x-1)(x-p)\r<BR>\n" );
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document.write( "(x^2-4)(x^2-px-x+p)\r<BR>\n" );
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document.write( "x^2(x^2-px-x+p)-4(x^2-px-x+p)\r<BR>\n" );
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document.write( "x^4-px^3-x^3+px^2-4x^2+4px+4x-4p\r<BR>\n" );
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document.write( "x^4+(-px^3-x^3)+(px^2-4x^2)+(4px+4x)-4p\r<BR>\n" );
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document.write( "x^4+(-p-1)x^3+(p-4)x^2+(4p+4)x-4p\r<BR>\n" );
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document.write( "Compare that result to 2Ax^4-Bx^3-Cx-16<BR>\n" );
document.write( "Match up the corresponding terms, and we have the following equations<BR>\n" );
document.write( "<ul><li>2Ax^4 = 1x^4 which leads to 2A = 1 and solves to A = 1/2 = 0.5</li><li>(-p-1)x^3 = -Bx^3 which leads -p-1 = -B and solves to B = p+1</li><li>(4p+4)x = -Cx which leads to 4p+4 = -C and solves to C = -4p-4</li><li>-4p = -16 which solves to p = 4</li></ul><BR>\n" );
document.write( "Use that value of p to find the other coefficients<BR>\n" );
document.write( "B = p+1 = 4+1 = 5<BR>\n" );
document.write( "C = -4p-4 = -4*4-4 = -20\r<BR>\n" );
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document.write( "The polynomial 2Ax^4-Bx^3-Cx-16 turns into x^4-5x^3+24x-16 after we plug in those A,B, and C values.\r<BR>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "A = 1/2 = 0.5<BR>\n" );
document.write( "B = 5<BR>\n" );
document.write( "C = -20\r<BR>\n" );
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document.write( " </SPAN>\n" );
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