document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=836899>Question 836899</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, \r<BR>\n" );
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document.write( "I am having trouble with the following question, ant help would be gratefully received.\r<BR>\n" );
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document.write( "Kind regards, \r<BR>\n" );
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document.write( "Hugh\r<BR>\n" );
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document.write( "Factorise the following expressions.\r<BR>\n" );
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document.write( "Question A\r<BR>\n" );
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document.write( "(i) x2 &#8722; x &#8722; 42 \r<BR>\n" );
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document.write( "(ii) 9m2 &#8722; 81n2 \r<BR>\n" );
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document.write( "Question B\r<BR>\n" );
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document.write( "In parts (i), (ii) below you should include each step in your<BR>\n" );
document.write( "reasoning and check that your solution is correct.\r<BR>\n" );
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document.write( "(i) Factorise then solve the equation x2 + 2x&#8722;24 = 0. \r<BR>\n" );
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document.write( "(ii) Explain how you could use your answer to part (B)(i) to solve the<BR>\n" );
document.write( "equation 7x2 + 14x&#8722;168 = 0.\r<BR>\n" );
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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 #504520 by </B><A HREF=/tutors/aboutme.mpl?userid=LinnW><B>LinnW(1048)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=LinnW><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=LinnW><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=504520\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Factorise the following expressions.<BR>\n" );
document.write( "Question A<BR>\n" );
document.write( "(i) x2 &#8722; x &#8722; 42<BR>\n" );
document.write( "(ii) 9m2 &#8722; 81n2<BR>\n" );
document.write( "Question B<BR>\n" );
document.write( "In parts (i), (ii) below you should include each step in your<BR>\n" );
document.write( "reasoning and check that your solution is correct.<BR>\n" );
document.write( "(i) Factorise then solve the equation x2 + 2x&#8722;24 = 0.<BR>\n" );
document.write( "(ii) Explain how you could use your answer to part (B)(i) to solve the<BR>\n" );
document.write( "equation 7x2 + 14x&#8722;168 = 0. \r<BR>\n" );
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document.write( "A(i) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+x+-+42 ALIGN=MIDDLE  ALT=\"x%5E2+-+x+-+42\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We want a pair of numbers such that their product is 42 and <BR>\n" );
document.write( "their sum is -1<BR>\n" );
document.write( "-7 and + 6 work for this and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+x+-+42 ALIGN=MIDDLE  ALT=\"x%5E2+-+x+-+42\"   DISABLED_style= \"max-width:90%; height:auto;\" > factored is<BR>\n" );
document.write( "(x - 7)(x + 6)<BR>\n" );
document.write( "A(ii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9m%5E2-81n%5E2 ALIGN=MIDDLE  ALT=\"9m%5E2-81n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Binomials of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-y%5E2 ALIGN=MIDDLE  ALT=\"x%5E2-y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > factor as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%29%28x-y%29 ALIGN=MIDDLE  ALT=\"%28x%2By%29%28x-y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so think of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9m%5E2-81n%5E2 ALIGN=MIDDLE  ALT=\"9m%5E2-81n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283m%29%5E2-%289n%29%5E2 ALIGN=MIDDLE  ALT=\"%283m%29%5E2-%289n%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which means the factors are<BR>\n" );
document.write( "(3m+9n)(3m-9n)<BR>\n" );
document.write( "B(i) x2 + 2x&#8722;24 = 0.<BR>\n" );
document.write( "Here we want a pair of numbers whose product is -24 and their sum is +2<BR>\n" );
document.write( "+6 and -4 work for this<BR>\n" );
document.write( "(x + 6)(x - 4) = 0<BR>\n" );
document.write( " B(ii)<BR>\n" );
document.write( "(ii) Explain how you could use your answer to part (B)(i) to solve the<BR>\n" );
document.write( "equation 7x2 + 14x&#8722;168 = 0. <BR>\n" );
document.write( "7 is a factor of each term, so 7x2 + 14x&#8722;168 = 0 factored is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%28x%5E2+%2B+2x+-+24%29+=+0+ ALIGN=MIDDLE  ALT=\"7%28x%5E2+%2B+2x+-+24%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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