document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1049745>Question 1049745</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,I have a question on polynomials..I've spent much time trying to figure out what to do,but I keep getting answers that don't add up in the end..Here is the question:\r<BR>\n" );
document.write( "\n" );
document.write( "The polynomial f(x) is given by f(x) =4x^3 +ax^2 + bx+2. (4x+1) is a factor of f(x).When f(x) is divided by (x-1) there is a remainder of 20. Find a and b.\r<BR>\n" );
document.write( "\n" );
document.write( "Please help,I'm so stuck.. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #665304 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=665304\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The polynomial f(x) is given by f(x) =4x^3 +ax^2 + bx+2. (4x+1) is a factor of f(x).When f(x) is divided by (x-1) there is a remainder of 20. Find a and b. <BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Using synthetic division::<BR>\n" );
document.write( "(-1/4)....4....a..........b..............2<BR>\n" );
document.write( ".........4...a-1..-(1/4)a+(1/4)+b....|(1/16)a-(1/16)-(1/4)b+b\r<BR>\n" );
document.write( "\n" );
document.write( "-------<BR>\n" );
document.write( "1st equation:: (1/16)a - (1/16) + (3/4)b = 0\r<BR>\n" );
document.write( "\n" );
document.write( "=====================================<BR>\n" );
document.write( "1)....4.....a......b......2<BR>\n" );
document.write( "......4....a+4...a+b+4...|.. a + b + 6<BR>\n" );
document.write( "----------------\r<BR>\n" );
document.write( "\n" );
document.write( "2nd equation:: a+b+6 = 20<BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "Solve 2nd eq for \"a\" and substitute in 1st to solve for \"b\"::<BR>\n" );
document.write( "a = 14-b<BR>\n" );
document.write( "----<BR>\n" );
document.write( "(1/16)(14-b) - (1/16) + (12/16)b = 0<BR>\n" );
document.write( "----<BR>\n" );
document.write( "14-b - 1 + 12b = 0<BR>\n" );
document.write( "----<BR>\n" );
document.write( "11b = -13<BR>\n" );
document.write( "b = -13/11<BR>\n" );
document.write( "----<BR>\n" );
document.write( "a = 14-b = 14+13/11 = 167/11<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "-------------- </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );