How do you factor perfect square trinomials?

Perfect square trinomials are quadratics obtained from squaring a binomial. Determining the binomial requires analyzing each term individually and then putting them together.

1. Determine if the first term has a coefficient

   x^2 + 10x + 25 If the first term in the trinomial has no coefficient, then the first term in the binomial is simply x. 9x^2 - 8x + 16 If the first term in the trinomial has a coefficient and it is a perfect square, then the first term is the root of the coefficient and x. In the above case, it would be 3x.

2. Determine the root of the last coefficient

   x^2 + 10x + 25 The last term is a perfect square, and in this case, its root is 5. 9x^2 - 8x + 16 The last term is a perfect square, and in this case, its root is 4.

3. Verify the middle coefficient is in agreement with the last

   x^2 + 10x + 25 Take the square root of the last coefficient and determine if its sum equals the middle coefficient. 5 + 5 = 10, thus it does. 9x^2 - 8x + 16 The square root in this case does not add up to the middle term, but if it is made negative, it adds up to -8.

4. Put all the terms together

   x^2 + 10x + 25 The first term is x, and the last is 5. The positive summation of the last equals the middle, so addition is used: (x + 5)^2. 9x^2 - 8x + 16 The first term is 3x, and the last is 4. The negative summation of the last equals the middle, so subtraction is used: (3x - 4)^2.