Question

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

Answer 1

Given:

The trinomial is

`c^2+2c+n`

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

`(a+b)^2=a^2+2ab+b^2` ...(i)

We have,

`c^2+2c+n` ...(ii)

From (i) and (ii), we get

`a^2=c^2, 2ab=2c, b^2=n`

`a=c`

Similarly,

`2ab=2c`

`2ab=2a`
`[\because a=c]`

`b=(2a)/(2a)`

`b=1`

Now,

`n=b^2`

`n=1^2`

`n=1`

The value of n is 1.

The trinomial is

`c^2+2c+1`

Splitting the middle term, we get

`=c^2+c+c+1`

`=c(c+1)+1(c+1)`

`=(c+1)(c+1)`

`=(c+1)^2`

Therefore, the factorized form of the trinomial is
`(c+1)^2`.