document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1081686>Question 1081686</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let f(x)=3x^4 + 7x^3 + ax^2 + bx -14 where a and b are constants.If (x-1) is a factor of f(x) and when f(x) is divided by (x+1), the remainder is -12, find the values of a and b. With these values of a and b,\r<BR>\n" );
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document.write( "(A) find a factor of f(x) in the form x+k where k is a postive integer.\r<BR>\n" );
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document.write( "(B) write f(x) in the form<BR>\n" );
document.write( "      f(x)=(x-1)(x+k)Q(x),where Q(x)is a real quadratic.\r<BR>\n" );
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document.write( "Hence,show that Q(x) is irreducible. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #696078 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=696078\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  f(x)=3x^4 + 7x^3 + ax^2 + bx -14 <BR>\n" );
document.write( "f(1)=0=3+7+a+b-14<BR>\n" );
document.write( "a+b=4<BR>\n" );
document.write( "f(-1)=-12=3-7+a-b-14<BR>\n" );
document.write( "a-b=6<BR>\n" );
document.write( "2a=10<BR>\n" );
document.write( "a=5<BR>\n" );
document.write( "b=1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C3x%5E4%2B7x%5E3%2B5x%5E2-x-14%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C3x%5E4%2B7x%5E3%2B5x%5E2-x-14%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(x+2) is a factor<BR>\n" );
document.write( "k=2<BR>\n" );
document.write( "(x^2+x-2) divides into 3x^4 + 7x^3 + ax^2 + bx -14 and that quotient is<BR>\n" );
document.write( "3x^2+4x+7<BR>\n" );
document.write( "(x-1)(x+2)(3x^2+4x+7)<BR>\n" );
document.write( "The roots of the quadratic term are complex<BR>\n" );
document.write( "the graph of it is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C3x%5E2%2B4x%2B7%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C3x%5E2%2B4x%2B7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The original polynomial has two real integer roots and two complex roots. </SPAN>\n" );
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