document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190367>Question 1190367</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Having trouble figuring out how to factor this problem.\r<BR>\n" );
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document.write( "Factor completely given that x-3 is a factor of x^3-5x^2-14x+60.\r<BR>\n" );
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document.write( "I tried grouping to factor and it isn't working. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #822135 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=822135\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Remainder Theorem:<BR>\n" );
document.write( "If p(x) is divided over (x-k), then p(k) is the remainder.\r<BR>\n" );
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document.write( "Comparing x-3 to x-k shows that k = 3<BR>\n" );
document.write( "p(x) = x^3-5x^2-14x+60<BR>\n" );
document.write( "p(3) = 3^3-5(3)^2-14(3)+60<BR>\n" );
document.write( "p(3) = 0<BR>\n" );
document.write( "A remainder of zero confirms that x-3 is indeed a factor of x^3-5x^2-14x+60\r<BR>\n" );
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document.write( "Here's the polynomial long division<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/EdjcLEZ.png\">\r<BR>\n" );
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document.write( "And here's what the synthetic division looks like<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/OeXSEvM.png\">\r<BR>\n" );
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document.write( "Either way, you should find that<BR>\n" );
document.write( "x^3-5x^2-14x+60 = (x-3)(x^2-2x-20)\r<BR>\n" );
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document.write( "You can use WolframAlpha or GeoGebra's CAS calculator to confirm. There are numerous other free calculators that will do the same type of thing.<BR>\n" );
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