Choose the constant term that completes the perfect square trinomial.

y 2 + 5y

+10/4

+25/4

+25/2

A perfect trinomial, if we begin by a binomial is defined as: the square of the first term, plus (or minus) the double product of the first term times the second, plus the square of the second term:

(a + b) ^2 = a^2 + 2ab + b^2

We are given:

y^2 + 5y + x

we need to find x, so x is defined as a squared quantity, which is equal to the second term coefficient (5) divided by 2, and that number squared, that is:

(5/2) ^2 = 25/4

that is the third term for the trinomial to be perfect.