Question

Find the zero of the following polynomial:

$p ( x ) = 3 x + 5$

Answer 1

For calculating the zero of a linear polynomial as given in your question, we add "= 0" after it.
So, 3x + 5 = 0, this means x = (-5/3). 
Hence, the zero of the polynomial is -5/3.

Answer 2

Equate the polynomial to zero
3x+5=0
3x = -5
x = -5/3