Find the value of n so that the expression is a perfect square trinomial. Then factor the trinomial. c²+2c+n
Determine the value of n

Given:

The trinomial is

To find:

The value of n for which the given trinomial is a perfect square and then factor the trinomial.

Solution:

We know that, the perfect square trinomial is given by

       ...(i)

We have,

       ...(ii)

From (i) and (ii), we get

Similarly,

Now,

The value of n is 1.

The trinomial is

Splitting the middle term, we get

Therefore, the factorized form of the trinomial is .