document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=718010>Question 718010</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The product of three consecutive integers is 21 more than the cube of the smallest integer. Find the integers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #440682 by </B><A HREF=/tutors/aboutme.mpl?userid=algebrahouse.com><B>algebrahouse.com(1659)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=algebrahouse.com><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=algebrahouse.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=440682\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = smallest integer<BR>\n" );
document.write( "x + 1 = second integer<BR>\n" );
document.write( "x + 2 = third integer {consecutive integers increase by 1}\r<BR>\n" );
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document.write( "x(x + 1)(x + 2) = x³ + 21  {product of the three is 21 more than cube of smallest}<BR>\n" );
document.write( "(x² + x)(x + 2) = x³ + 21 {used distributive property}<BR>\n" );
document.write( "x³ + 3x² + 2x = x³ + 21  {used foil method}<BR>\n" );
document.write( "3x² + 2x = 21 {subtracted x³ from each side}<BR>\n" );
document.write( "3x² + 2x - 21 = 0 {subtracted 21 from each side}<BR>\n" );
document.write( "3x² + 9x - 7x - 21 = 0 {split 2x into 9x and -7x}<BR>\n" );
document.write( "3x(x + 3) - 7(x + 3) = 0 {factored 3x out of first two terms and -7 out of last two terms}<BR>\n" );
document.write( "(3x - 7)(x + 3) = 0 {factored x + 3 out of the two terms}<BR>\n" );
document.write( "3x - 7 = 0 or x + 3 = 0 {set each factor equal to 0}<BR>\n" );
document.write( "x = 7/3 or x = -3 {solved each equation for x}<BR>\n" );
document.write( "x = -3 {fractions are not integers}<BR>\n" );
document.write( "x + 1 = -2 {substituted -3, in for x, into x + 1}<BR>\n" );
document.write( "x + 2 = -1 {substituted -1, in for x, into x + 2}\r<BR>\n" );
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document.write( "-3, -2, and -1 are the three consecutive integers<BR>\n" );
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