Answer
prime
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.
