document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=41508>Question 41508</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321286960/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> During a lesson on factoring natural number, Marcia said, \"I think when you factor an odd number, you always get odd factor.\"  <BR>\n" );
document.write( "a, Is Marcia correct?<BR>\n" );
document.write( "b, How could you convince Marcia and the rest of the class that Marcia is or is not correct. </SPAN>\n" );
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document.write( "If you have an odd number it has the form 2a+1<BR>\n" );
document.write( "Assume that 2a+1 has an even factor, 2b and another<BR>\n" );
document.write( "factor which may or may not be even.<BR>\n" );
document.write( "If the 2nd factor is even, 2c then 2b(2c)=2a+1<BR>\n" );
document.write( "Then 2(b2c)=2a+1<BR>\n" );
document.write( "But 2(b2c) is even so cannot equal 2a+1.<BR>\n" );
document.write( "If the 2nd factor is odd, 2c+1, then 2b(2c+1)=2a+1<BR>\n" );
document.write( "Then 2[b(2c+1)]=2a+1<BR>\n" );
document.write( "But 2[b(2c+1)] is even and cannot equal 2a+1.<BR>\n" );
document.write( "Therefore the factors of every odd number are odd.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );