# Is  a perfect square trinomial and how do you factor it?

##### 1 Answer
May 31, 2015

You seem to have lost your trinomial from the question, so let me address the general question.

How do you recognise a perfect square trinomial and how do you factor it?

A perfect square trinomial is the square of a binomial. A general binomial is of the form $a + b$, so we need to look at:

${\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$

So a trinomial is a perfect square trinomial if the following three conditions hold:

(1) The first term is a square.
(2) The last term is a square.
(3) The middle term is twice the product of square roots (positive or negative) of the first and last term.

For example, $16 {x}^{2} - 24 x + 9$ is a perfect square trinomial:

(1) $16 {x}^{2} = {\left(4 x\right)}^{2}$
(2) $9 = {3}^{2}$
(3) $- 24 x = 2 \times \left(4 x\right) \times - 3$

To factor such a trinomial:
(1) Take the positive square root of the first term (e.g. $4 x$)
(2) Take the square root of the second term whose sign matches that of the middle term. (e.g. $- 3$)
(3) Add them together to get your repeated factor (e.g. $\left(4 x - 3\right)$)