document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1036514>Question 1036514</A>: <I><SPAN STYLE=\"word-break: break-all;\"> let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+2x%5E3+-+7x+%2B2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+2x%5E3+-+7x+%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "A) calculate f(0), f(1), f(2), f(-1), and f(-2). which of these is useful in factorizing f?<BR>\n" );
document.write( "B) from the previous part, you have a factor x - a of f(x) for some a. then you can write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E3+-+7x+%2B2+=+%28x-a%29Multiply%28Ax%5E2+%2B+Bx+=+C%29 ALIGN=MIDDLE  ALT=\"2x%5E3+-+7x+%2B2+=+%28x-a%29Multiply%28Ax%5E2+%2B+Bx+=+C%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "for some choice of numbers A, B, and C. two of the numbers can be determined by inspection - that is, by looking. which two?<BR>\n" );
document.write( "C)by considering the x^2 term (or the x term) on the right hand side, and match with the corresponding piece on the left hand side, compute the remaining number of A, B, and C that you have not yet determined.<BR>\n" );
document.write( "D) solve f(x) = 0<BR>\n" );
document.write( "E) sketch <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+2x%5E3+-+7x+%2B2 ALIGN=MIDDLE  ALT=\"y=+2x%5E3+-+7x+%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "F) use your sketch to solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E3+-+7x+%2B2%3C0 ALIGN=MIDDLE  ALT=\"2x%5E3+-+7x+%2B2%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\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 #651225 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=651225\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A) f(0) = 2, f(1) = -3, f(2) = 4, f(-1) = 7, and f(-2) = 0, all determined by direct substitution.\r<BR>\n" );
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document.write( "B)   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E3+-+7x+%2B2+=+%28x-a%29%2A%28Ax%5E2+%2B+Bx+%2BC%29 ALIGN=MIDDLE  ALT=\"2x%5E3+-+7x+%2B2+=+%28x-a%29%2A%28Ax%5E2+%2B+Bx+%2BC%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "From part (A), we find that -2 is a zero of f(x), and so x + 2 is a factor of f(x).<BR>\n" );
document.write( "==>  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E3+-+7x+%2B2+=+%28x%2B2%29%2A%28Ax%5E2+%2B+Bx+%2BC%29 ALIGN=MIDDLE  ALT=\"2x%5E3+-+7x+%2B2+=+%28x%2B2%29%2A%28Ax%5E2+%2B+Bx+%2BC%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Also, it is quite easy to see that A = 2, and the constant C has to be C = 1.\r<BR>\n" );
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document.write( "==>   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E3+-+7x+%2B2+=+%28x%2B2%29%2A%282x%5E2+%2B+Bx+%2B1%29 ALIGN=MIDDLE  ALT=\"2x%5E3+-+7x+%2B2+=+%28x%2B2%29%2A%282x%5E2+%2B+Bx+%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "C)  Expanding the right-hand side but considering only the coefficient of 0 of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28B%2B4%29x%5E2+=+0 ALIGN=MIDDLE  ALT=\"%28B%2B4%29x%5E2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "==> B = -4.\r<BR>\n" );
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document.write( "D)  Thus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E3+-+7x+%2B2+=+%28x%2B2%29%2A%282x%5E2+-4x+%2B1%29 ALIGN=MIDDLE  ALT=\"2x%5E3+-+7x+%2B2+=+%28x%2B2%29%2A%282x%5E2+-4x+%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The other two zeros are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282+%2B-+sqrt%282+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-+sqrt%282+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "E)  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+2x%5E3+-+7x+%2B2%29 ALIGN=MIDDLE  ALT=\"graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+2x%5E3+-+7x+%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "F)  This is easy and so I leave this up to you. (Look at the parts of the graph that are below the x-axis.) </SPAN>\n" );
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