document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201744>Question 1201744</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write a trinomial that has a GCF of 7x to exponent of 2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #836255 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</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=836255\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer: 21x^4 + 28x^3 + 35x^2<BR>\n" );
document.write( "Other answers are possible.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Explanation:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Pick any trinomial where the coefficients are relatively prime to one another<BR>\n" );
document.write( "This means the GCF of the coefficients is 1.<BR>\n" );
document.write( "Let's say we go for 3x^2+4x+5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Multiply that with 7x^2<BR>\n" );
document.write( "7x^2(3x^2+4x+5)<BR>\n" );
document.write( "7x^2*3x^2 + 7x^2*4x + 7x^2*5 ... distributive property<BR>\n" );
document.write( "21x^4 + 28x^3 + 35x^2<BR>\n" );
document.write( "This leads to an expression where we are guaranteed to have 7x^2 as the GCF of each term of the trinomial.<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );