document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=985473>Question 985473</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let P(x)=x^3-2x^2-13x-10<BR>\n" );
document.write( "a.determine whether x-5 is a factor if P(x).<BR>\n" );
document.write( "b.find another factor of P(x).<BR>\n" );
document.write( "c.find a complete factorization of P(x).<BR>\n" );
document.write( "d. Solve the equation P(x)=0. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #606343 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52790)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=606343\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "a. &nbsp;To determine whether &nbsp;x-5&nbsp; is a factor of &nbsp;P(x), &nbsp;calculate &nbsp;P(5), &nbsp;i.e. &nbsp;simply substitute the value of &nbsp;5&nbsp; into the polynomial. &nbsp;You will get \r<BR>\n" );
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document.write( "P(5) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E3+-+2%2A5%5E2+-+13%2A5+-+10 ALIGN=MIDDLE  ALT=\"5%5E3+-+2%2A5%5E2+-+13%2A5+-+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 125 - 50 - 65 - 10 = 0.\r<BR>\n" );
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document.write( "According wi the &nbsp;<B>Remainder Theorem</B>&nbsp; (see, &nbsp;for example, &nbsp;the lesson &nbsp;<A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Divisibility-of-polynomial-f%28x%29-by-binomial-x-a.lesson>Divisibility of polynomial f(x) by binomial x-a</A>&nbsp; in this site), &nbsp;the binom &nbsp;x-5&nbsp; is a factor of the polynomial &nbsp;P(x).\r<BR>\n" );
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document.write( "b. &nbsp;Make the long division of the polynomial &nbsp;P(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3-2x%5E2-13x-10 ALIGN=MIDDLE  ALT=\"x%5E3-2x%5E2-13x-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; by &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29 ALIGN=MIDDLE  ALT=\"%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. &nbsp;You will get \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3-2x%5E2-13x-10 ALIGN=MIDDLE  ALT=\"x%5E3-2x%5E2-13x-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29 ALIGN=MIDDLE  ALT=\"%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+%2B+3x+%2B+2%29 ALIGN=MIDDLE  ALT=\"%28x%5E2+%2B+3x+%2B+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "So, &nbsp;the polynomial &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+%2B+3x+%2B+2%29 ALIGN=MIDDLE  ALT=\"%28x%5E2+%2B+3x+%2B+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; is another factor of the polynomial &nbsp;P(x). \r<BR>\n" );
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document.write( "c. &nbsp;The quadratic polynomial &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+3x+%2B+2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+3x+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; has the roots &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -1&nbsp; and &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D ALIGN=MIDDLE  ALT=\"x%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -2&nbsp; (use the quadratic formula &nbsp;<A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/quadratic/lessons/Introduction-Into-Quadratics.lesson>Introduction into Quadratic Equations</A>&nbsp; or the Vieta's theorem &nbsp;<A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/quadratic/lessons/Solving-quadratic-equations-without-quadratic-formula.lesson>Solving quadratic equations without quadratic formula</A>, &nbsp;lessons in this site)\r<BR>\n" );
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document.write( "It implies that &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+3x+%2B+2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+3x+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Therefore, \r<BR>\n" );
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document.write( "P(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29 ALIGN=MIDDLE  ALT=\"%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "is the complete factorization of the polynomial &nbsp;P(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3-2x%5E2-13x-10 ALIGN=MIDDLE  ALT=\"x%5E3-2x%5E2-13x-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "d. &nbsp;Since P(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3-2x%5E2-13x-10 ALIGN=MIDDLE  ALT=\"x%5E3-2x%5E2-13x-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29 ALIGN=MIDDLE  ALT=\"%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, &nbsp;the roots of the polynomial <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3-2x%5E2-13x-10 ALIGN=MIDDLE  ALT=\"x%5E3-2x%5E2-13x-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > are 5, -1 and -2. \r<BR>\n" );
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document.write( "The solution is completed.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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