perfect square trinomial
a trinomial that is the result of squaring a binomial
A perfect square trinomial is a mathematical expression in the form of ax^2 + bx + c that can be factored into a binomial squared, which means it can be written as (px + q)^2 where p and q are constants.
To determine if a trinomial is a perfect square, we first need to check the coefficient of the x^2 term (a). If a is a perfect square (i.e., the square of an integer), then it is possible that the trinomial is a perfect square. Next, we need to check that the constant term (c) is also a perfect square. Finally, we check that the coefficient of the x term (b) is twice the product of the square root of a and the square root of c.
For example, consider the trinomial x^2 + 6x + 9. Here, the coefficient of the x^2 term is 1, which is a perfect square and the constant term is 9, which is also a perfect square. Further, the coefficient of the x term is twice the product of the square root of 1 and the square root of 9 (which is equal to 6), i.e., 6 = 2*(1)*(3), confirming that it is a perfect square trinomial. It can be factored as (x + 3)^2.
Overall, the key to identifying perfect square trinomials is knowing the conditions that they must satisfy and applying these conditions to verify if the trinomial is indeed a perfect square.
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