Question

Why don't we take the co-efficient as zero in a polynomial like x?

Answer 1

We don't take co-efficient AS zero in polynomial like x because:
(0)x=0 but x can be any real number
                        AND
(1)x=x (the value remains same here)

Answer 2

if u take co-efficient as zero the polynomial becomes zero
for example
ax^2 +bx+c is a quadratic expression
if u take co-efficients a and b are zeroes
it become c in that we don't have x