Substitute 2 for x in 



and see if we get 0.  If so, 2 is a zero of P(x).
But if not, 2 is not a zero of P(x).






Yes, 2 is a zero of P(x), for we got 0 when we 
substituted 2 for x.

Maybe your teacher wanted you to use the synthetic
division method for substituting instead of
directly substituting. If so then use this method
for substituting 2 instead of directly substituting.
Write the 2 on the left and the coefficients of x
in order on the right, and draw this array:

   2 | 1  2  -29  42
     |
      --------------

Bring down the 1

   2 | 1  2  -29  42
     |
      --------------
       1

Multiply the 1 by the 2 on the left,
getting 2, and write it above and to the right
of the 1, under the upper 2, like this:

   2 | 1  2  -29  42
     |    2
      --------------
       1

Now add the 2+2, getting 4 and write it below the
two 2's beside the 1, like this:

   2 | 1  2  -29  42
     |    2
      --------------
       1  4

Multiply the 4 by the 2 on the left,
getting 8, and write it above and to the right
of the 4, under the -29, like this:

   2 | 1  2  -29  42
     |    2    8
      --------------
       1  4

Now add the -29+8, getting -21 and write it below the
-29 and the 8 beside the 4, like this:

   2 | 1  2  -29  42
     |    2    8
      --------------
       1  4  -21

Multiply the -21 by the 2 on the left,
getting -42, and write it above and to the right
of the -21, under the 42, like this:

   2 | 1  2  -29  42
     |    2    8 -42
      --------------
       1  4  -21

Now add the 42-42, getting 0 and write it below the
42 and the -42 beside the -21, like this:

   2 | 1  2  -29  42
     |    2    8 -42 
      --------------
       1  4  -21   0

That bottom right number is always the same as what
you get when you substitute 2 for x in the polynomial.

The reason your teacher wants you to learn this method
for substituting, instead of the easier method of 
directly substituting is because synthetic division has
other uses, and sometimes it's actually easier than
directly substituting.

Edwin