y=f(x)=(x+ 1)*(x-a)

Because the above function is even, f(x)=f(-x).

That is, (x+1) * (x-a) = (-x+1) * (-x-a)

The expanded x 2-ax+x-a = x 2+ax-x-a, so that x(a- 1)=0 holds.

Therefore, a= 1.

Quick solution:

Because it is an even function, f( 1)=f(- 1).

Substitution and solution get a= 1.