## Factoring Trinomials

The polynomial

Ultimately, the trinomial should be factored in the form ^{2}.
Additionally, the sum of products

## Perfect Squares

Some trinomials, known as perfect square trinomials, can be factored into two equal binomials. For example:

and

Perfect square trinomials always factor as the square of a binomial.

To recognize a perfect square trinomial, look for the following features:

- The first and last terms are perfect squares.
- The middle term is divisible by 2.

For example, ^{2} is the square of x, and 25 is the square of 5.
The middle term (-10x) is divisible by 2 (equalling -5x).

Given that the coefficient of x^{2} is 1, we know that the factored form will be ^{2}.
This is a perfect square.