document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1004098>Question 1004098</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which of the following is a factor of (x^4-27x^2-14x+120)\r<BR>\n" );
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document.write( "A. x+2 , B. x-3 , C. x+4 , D. x+5<BR>\n" );
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document.write( "Simplify (x^3+5x^2+5x-2) divided by (x+2).\r<BR>\n" );
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document.write( "A, x^2-3x-1 , B. x^2-3x+1, C. x^2+3x-1 , D. x^2+3x+1\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 #620640 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=620640\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do the first problem to get you started.\r<BR>\n" );
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document.write( "The best way to do this problem is to check each answer choice\r<BR>\n" );
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document.write( "Let's check choice A. This factor is x+2, so solve x+2 = 0 to get x = -2\r<BR>\n" );
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document.write( "Plug in x = -2 and evaluate\r<BR>\n" );
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document.write( "y = x^4-27x^2-14x+120\r<BR>\n" );
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document.write( "y = (-2)^4-27(-2)^2-14(-2)+120 ... replace each x with -2\r<BR>\n" );
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document.write( "y = 56\r<BR>\n" );
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document.write( "The result y = 56 is NOT zero, so x = -2 is NOT a root of the polynomial.\r<BR>\n" );
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document.write( "Since x = -2 is NOT a root of the polynomial, this means x+2 is NOT a factor of the polynomial.\r<BR>\n" );
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document.write( "Let's check choice B. This factor is x-3, so solve x-3 = 0 to get x = 3\r<BR>\n" );
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document.write( "Plug in x = 3 and evaluate\r<BR>\n" );
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document.write( "y = x^4-27x^2-14x+120\r<BR>\n" );
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document.write( "y = (3)^4-27(3)^2-14(3)+120 ... replace each x with 3\r<BR>\n" );
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document.write( "y = -84\r<BR>\n" );
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document.write( "The result y = -84 is NOT zero, so x = 3 is NOT a root of the polynomial.\r<BR>\n" );
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document.write( "Since x = 3 is NOT a root of the polynomial, this means x-3 is NOT a factor of the polynomial.\r<BR>\n" );
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document.write( "Let's check choice C. This factor is x+4, so solve x+4 = 0 to get x = -4\r<BR>\n" );
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document.write( "Plug in x = -4 and evaluate\r<BR>\n" );
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document.write( "y = x^4-27x^2-14x+120\r<BR>\n" );
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document.write( "y = (-4)^4-27(-4)^2-14(-4)+120 ... replace each x with -4\r<BR>\n" );
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document.write( "y = 0\r<BR>\n" );
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document.write( "The result y = 0 is zero, so x = -4 is definitely a root of the polynomial.\r<BR>\n" );
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document.write( "Since x = -4 is a root of the polynomial, this means x+4 is a factor of the polynomial.\r<BR>\n" );
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document.write( "Let's check choice D. This factor is x+5, so solve x+5 = 0 to get x = -5\r<BR>\n" );
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document.write( "Plug in x = -5 and evaluate\r<BR>\n" );
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document.write( "y = x^4-27x^2-14x+120\r<BR>\n" );
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document.write( "y = (-5)^4-27(-5)^2-14(-5)+120 ... replace each x with -5\r<BR>\n" );
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document.write( "y = 140\r<BR>\n" );
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document.write( "The result y = 140 is NOT zero, so x = -5 is NOT a root of the polynomial.\r<BR>\n" );
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document.write( "Since x = -5 is NOT a root of the polynomial, this means x+5 is NOT a factor of the polynomial.\r<BR>\n" );
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document.write( "Summary:\r<BR>\n" );
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document.write( "Only x+4 is a factor of the polynomial. So only choice C is the answer. </SPAN>\n" );
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