Work Step by Step
RECALL: A perfect square trinomial can be factored using either of the following formulas: (i) $a^2+2ab+b^2=(a+b)^2$; or (ii) $a^2-2ab+b^2=(a-b)^2$ The given trinomial can be written as: $=x^2-9xy + (9y)^2$ This trinomial is not similar to any of the perfect square trinomials in (i) and (ii). Thus, this trinomial is NOT a perfect square trinomial. This trinomial has a leading coefficient of 1. A quadratic trinomial with a leading coefficient of $1$ can be factored only if there are factors of the numerical coefficient of the third term whose sum is equal to the numerical coefficient of the middle term. However, $81$ has no pair of factors whose sum is equal to $-9$. There are also no common factors for the terms in the trinomial. This means that the given trinomial is prime.