Question

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

Answer 1

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:

`(a+b)^2 = a^2 + 2ab + 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, `16x^2 - 24x + 9` is a perfect square trinomial:

(1) `16x^2 = (4x)^2`
(2) `9 = 3^2`
(3) `-24x = 2xx(4x)xx-3`

To factor such a trinomial:
(1) Take the positive square root of the first term (e.g. `4x`)
(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. `(4x-3)`)