document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=253630>Question 253630</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For p(x)= 4x^5 + 4x^4 + 25x^3 - 56x^2 - 74x - 20\r<BR>\n" );
document.write( "\n" );
document.write( "a. Factor into linear and irreducible quadratic factors<BR>\n" );
document.write( "b. Factor completely<BR>\n" );
document.write( "c. Find all zeros </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #185995 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=185995\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here is pour problem:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E5+%2B+4x%5E4+%2B+25x%5E3+-+56x%5E2+-+74x+-+20 ALIGN=MIDDLE  ALT=\"4x%5E5+%2B+4x%5E4+%2B+25x%5E3+-+56x%5E2+-+74x+-+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To factor I would first apply: P, N, I using the following table:<BR>\n" );
document.write( "P . . . . . N . . . . I<BR>\n" );
document.write( "1 . . . . .4 . . . . .0<BR>\n" );
document.write( "we have a couple other choices as<BR>\n" );
document.write( "P . . . . . N . . . . I<BR>\n" );
document.write( "1 . . . . . 2 . . . . 2<BR>\n" );
document.write( "1 . . . . . 0 . . . . 4.<BR>\n" );
document.write( "We must have a positive root somewhere. Now I turn to P / Q.<BR>\n" );
document.write( "The factors of 20 = 1, 2, 4, 5, 10, 20<BR>\n" );
document.write( "The factors of 4  = 1, 2, 4.<BR>\n" );
document.write( "P/Q means each numerator over each denominator as:<BR>\n" );
document.write( "1, 1/2, 1/4, 2, 4, 5, 5/2, 5/4, 10, 5, 2.5, 20.<BR>\n" );
document.write( "Through trial and error, we get X = 2, x = -1/2, x = -1/2<BR>\n" );
document.write( "By synthetic division\r<BR>\n" );
document.write( "\n" );
document.write( "2 [4 . . .4 . . .25 . . . -56 . . . -74 . . . -20]\r<BR>\n" );
document.write( "\n" );
document.write( " . 4 . . .12 . . .49 . . .42 . . . . 10 . . .r = 0\r<BR>\n" );
document.write( "\n" );
document.write( "-1/2 . [4 . . .12 . . .49 . . .42 . . . . 10]\r<BR>\n" );
document.write( "\n" );
document.write( " . . . .4 . . .10 . . .44 . . .20 . . . r = 0]\r<BR>\n" );
document.write( "\n" );
document.write( "-1/2 . [4 . . .10 . . .44 . . .20]\r<BR>\n" );
document.write( "\n" );
document.write( " . . . 4 . . . 8 . . . 40 . . .r = 0\r<BR>\n" );
document.write( "\n" );
document.write( "We have the quadratic function of<BR>\n" );
document.write( "4x^2 + 8x + 40<BR>\n" );
document.write( "--<BR>\n" );
document.write( "part a: Linear and irreducible.<BR>\n" );
document.write( "Using quadratic<BR>\n" );
document.write( "4x^2 + 8x + 40<BR>\n" );
document.write( "becomes<BR>\n" );
document.write( "(2x - (-4+13i))*(2x - (-4-13i))<BR>\n" );
document.write( "so, we have<BR>\n" );
document.write( "(x-2)(2x+1)*(2x+1)*(2x - (-4+13i))*(2x - (-4-13i))\r<BR>\n" );
document.write( "\n" );
document.write( "--<BR>\n" );
document.write( "part b: factor completely<BR>\n" );
document.write( "To me a and b are the same:<BR>\n" );
document.write( "(x-2)(2x+1)*(2x+1)(2x - (-4+13i))(2x - (-4+13i))<BR>\n" );
document.write( "--<BR>\n" );
document.write( "part c: all zero's<BR>\n" );
document.write( "X = 2, -1/2, -1/2, (-4 + 13i)/2, (-4 - 13i)/2\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );