Given that \ \

\

\"\" \ \

\

If p/q is a rational zero, then p is a factor of 4 and q is a factor of 2. \ \

\

The possible values of p are   ± 1,  ± 2, ± 4

\

The possible values for q are ± 1 , ± 2

\

By the Rational Roots Theorem, the only possible rational roots are, p/q = ± 1,   ± 2,   ±4

\

Make a table for the synthetic division and test possible real zeros.

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\

       p/q

\ 		\

2

\ 		    -6    5 \

4

\
       1 \

2

\ 		     -4     1 \

      5

\
       2       2     -2     1      6
       4 \

2

\ 		     2    13 \

      56

\
      -1      2       -8    13      -9
      -2 \

2

\ 		    -10    25 \

 -46

\
       -4 \

2

\ 		    -14    61 \

-240

\
\

Therefore there is no possible rational zero for the given polynomial function. \ \