document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=65095>Question 65095</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (a + 2b)^2  <BR>\n" );
document.write( "= a^2 + 4b^2  <BR>\n" );
document.write( " = a^2 + 4ab + 4b^2  <BR>\n" );
document.write( " = a^2 + 2ab + 2b^2  <BR>\n" );
document.write( " cannot be multiplied out any further  \r<BR>\n" );
document.write( "\n" );
document.write( "4x^2 + 9   <BR>\n" );
document.write( "= (2x + 3)^2  <BR>\n" );
document.write( " = (4x + 9)^2  <BR>\n" );
document.write( " = (3x + 2)^2  <BR>\n" );
document.write( " cannot be factored<BR>\n" );
document.write( " <BR>\n" );
document.write( "Factor the expression  4x^2 - 9 . \r<BR>\n" );
document.write( "\n" );
document.write( "Factor the expression   9x^2 - 12x + 4 \r<BR>\n" );
document.write( "\n" );
document.write( "Factor  16x^2 + 40xy + 25y^2<BR>\n" );
document.write( " <BR>\n" );
document.write( "8x^3 + 1  <BR>\n" );
document.write( "= (2x + 1)(4x^2 - 2x + 1)  <BR>\n" );
document.write( " = (2x - 1)(4x^2 + 2x + 1)  <BR>\n" );
document.write( " = (2x + 1)(4x^2 + 2x - 1)  <BR>\n" );
document.write( " cannot be factored because it is the sum of two cubes \r<BR>\n" );
document.write( "\n" );
document.write( "Factor the expression   x^3  +  8y^3  \r<BR>\n" );
document.write( "\n" );
document.write( " Factor the expression   x^9  -  27y^6 \r<BR>\n" );
document.write( "\n" );
document.write( "You are told that f(x) is a polynomial, and you are told that when we divide  x+1  into f(x) then the remainder is 0.  Based on this information, which of these statements is necessarily true?  f(1) = 0  <BR>\n" );
document.write( " f(0) = 1  <BR>\n" );
document.write( " f(-1) = 0  <BR>\n" );
document.write( " f(0) = -1  \r<BR>\n" );
document.write( "\n" );
document.write( "   <BR>\n" );
document.write( "Divide  x + 1  into  f(x) = 2x^3 + 3x^2 + 9x + 5.    Write your answer in the form given by the Division Algorithm; in other words, write your answer as:    2x^3 + 3x^2 + 9x + 5  =  q(x)(x+1) + r(x)  for some polynomials q(x) and r(x).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #45602 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=45602\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a + 2b)^2 <BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "= a^2 + 4ab + 4b^2 <BR>\n" );
document.write( "cannot be multiplied out any further <BR>\n" );
document.write( "4x^2 + 9 <BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "cannot be factored in the Real Number System\r<BR>\n" );
document.write( "\n" );
document.write( "Factor the expression 4x^2 - 9 <BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "(2x-3)(2x+3)<BR>\n" );
document.write( "----------------- <BR>\n" );
document.write( "Factor the expression 9x^2 - 12x + 4 <BR>\n" );
document.write( "=(3x-2)^2<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "Factor 16x^2 + 40xy + 25y^2<BR>\n" );
document.write( "=(4x+5y)^2<BR>\n" );
document.write( "------------\r<BR>\n" );
document.write( "\n" );
document.write( "8x^3 + 1<BR>\n" );
document.write( "Answer: <BR>\n" );
document.write( "= (2x + 1)(4x^2 - 2x + 1) <BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Factor the expression x^3 + 8y^3<BR>\n" );
document.write( "=(x+2y)(x^2-2xy+4y^2)<BR>\n" );
document.write( "----------------------- <BR>\n" );
document.write( "Factor the expression x^9 - 27y^6 <BR>\n" );
document.write( "=(x^3-3y^2)(x^6-3x^3y^2+9y^4)<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "You are told that f(x) is a polynomial, and you are told that when we divide x+1 into f(x) then the remainder is 0. Based on this information, which of these statements is necessarily true? <BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "f(-1) = 0 <BR>\n" );
document.write( "-------------\r<BR>\n" );
document.write( "\n" );
document.write( "Divide x + 1 into f(x) = 2x^3 + 3x^2 + 9x + 5. Write your answer in the form given by the Division Algorithm; in other words, write your answer as: 2x^3 + 3x^2 + 9x + 5 = q(x)(x+1) + r(x) for some polynomials q(x) and r(x).<BR>\n" );
document.write( "If you know synthetic division:<BR>\n" );
document.write( "-1)....2....3....9....5<BR>\n" );
document.write( ".......2....1....8.|.-3<BR>\n" );
document.write( "f(x)=(2x^2+x+8)(x+1)-3<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );