document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189362>Question 1189362</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider g(x) = 2x^3 - x^2 + 2x -1\r<BR>\n" );
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document.write( "(a) Tell the maximum number of real zeros that the function may have. Do not <BR>\n" );
document.write( "    attempt to find the zeros.<BR>\n" );
document.write( "(b) List the potential rational zeros. Do not attempt to find the zeros.<BR>\n" );
document.write( "(c) Determine the real zeros of g and write g in factored form. </SPAN>\n" );
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document.write( "(a) A polynomial of degree n has a maximum of n real zeros.  This polynomial is degree 3, so the maximum number of real zeros is 3.<br><BR>\n" );
document.write( "(b) (+/-) (p/q), where p is a factor of the constant term (-1) and q is a factor of the leading coefficient (2). So the possible rational zeros are<BR>\n" );
document.write( "1, -1, 1/2, and -1/2.<br><BR>\n" );
document.write( "(c) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E3-x%5E2%2B2x-1=0 ALIGN=MIDDLE  ALT=\"2x%5E3-x%5E2%2B2x-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The coefficients 2, -1, 2, -1 show us this can easily be factored by grouping:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%5E3-x%5E2%29%2B%282x-1%29=0 ALIGN=MIDDLE  ALT=\"%282x%5E3-x%5E2%29%2B%282x-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%282x-1%29%2B1%282x-1%29=0 ALIGN=MIDDLE  ALT=\"x%5E2%282x-1%29%2B1%282x-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B1%29%282x-1%29=0 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B1%29%282x-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The factor (x^2+1) produces a pair of complex roots.  The only real root is 1/2, coming from the factor (2x-1).<br><BR>\n" );
document.write( " </SPAN>\n" );
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