document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=101639>Question 101639</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A) Factor each polynomial completely, given that the binomial following it is a factor of the polynomial. \r<BR>\n" );
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document.write( "X^3 + 2x^2 – 5x – 6, x+3\r<BR>\n" );
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document.write( "B) Factor each difference or sum of cubes. \r<BR>\n" );
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document.write( "U^3 – 125v^3\r<BR>\n" );
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document.write( "C) Factor each polynomial completely. If a polynomial is prime, say so. \r<BR>\n" );
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document.write( "1)  32a^2 + 4a -6\r<BR>\n" );
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document.write( "2)  9bn^3 + 15bn^2 – 14bn\r<BR>\n" );
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document.write( "Any help would be greatly appreciated. I need to figure these out so I can finish my project. Thank you so much. Step by step explanations would be even better, so I can learn how to do this on my own.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #73944 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=73944\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A) Factor each polynomial completely, given that the binomial following it is a factor of the polynomial. \r<BR>\n" );
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document.write( "X^3 + 2x^2 – 5x – 6, x+3<BR>\n" );
document.write( "Using synthetic division:<BR>\n" );
document.write( "-3)....1....2....-5....-6<BR>\n" );
document.write( "........1....-1....-2..|..0\r<BR>\n" );
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document.write( "Quotient: x^2-x-2<BR>\n" );
document.write( "Remainder: 0<BR>\n" );
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document.write( "Factoring the Quotient:<BR>\n" );
document.write( "(x-2)(x+1)<BR>\n" );
document.write( "Therefore: f(x) = (x+3)(x-2)(x+1)<BR>\n" );
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document.write( "B) Factor each difference or sum of cubes.<BR>\n" );
document.write( "Form: a^3-b^3 = (a-b)(a^2+ab+b^2<BR>\n" );
document.write( "Your Problem:<BR>\n" );
document.write( "U^3 – 125v^3 = (U-5V)(U+5VU+25v^2)<BR>\n" );
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document.write( "C) Factor each polynomial completely. If a polynomial is prime, say so. \r<BR>\n" );
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document.write( "1)  32a^2 + 4a -6<BR>\n" );
document.write( "= 2(16a^2+2a-3)<BR>\n" );
document.write( "= 2(16a^2+8a-6a-3)<BR>\n" );
document.write( "= 2(8a(2a+1)-3(2a+1)<BR>\n" );
document.write( "= 2(2a+1)(8a-3)<BR>\n" );
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document.write( "2)  9bn^3 + 15bn^2 – 14bn<BR>\n" );
document.write( "= bn(9n^2+15n-14)<BR>\n" );
document.write( "= bn(3n-2)(3n+7)<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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