Work Step by Step
RECALL: A perfect square trinomial can be factored using either of the following formulas: (i) $a^2+2ab+b^2= (a+b)^2$ (ii) $a^2-2ab+b^2=(a-b)^2$ The given trinomial can be written as: $=x^2-7x + 7^2$ This trinomial is not in the same form as either of the perfect square trinomials in formulas (i) and (ii). Thus, the given trinomial is not a perfect square trinomial so it cannot be factored using formulas (i) and (ii). The trinomial cannot be factored because $49$ has no factors whose sum is equal to the numerical coefficient of the middle term. Therefore the given trinomial is prime.