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