Question 1189362
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(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>
(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
1, -1, 1/2, and -1/2.<br>
(c) {{{2x^3-x^2+2x-1=0}}}<br>
The coefficients 2, -1, 2, -1 show us this can easily be factored by grouping:<br>
{{{(2x^3-x^2)+(2x-1)=0}}}
{{{x^2(2x-1)+1(2x-1)=0}}}
{{{(x^2+1)(2x-1)=0}}}<br>
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>