Answer:
No it's not.
Step-by-step explanation:
A perfect square quadratic trionmial is typically in the form of
a²x² ± 2abx + b², which can be written as (ax ± b)². But it's not possible to write x²-2x-24 in this form:
(1)x² -2(1)x + 1² - 23
Because of this additional subtraction of 23 in the expression, the trinomial is not a perfect square.
In fact, if you go on factoring the given trinomial, you will get two distinct factors:
x² -2x -24
= x² -6x + 4x -24
= x (x - 6) +4 (x - 6)
= (x - 6) (x + 4)
In contrast, if you factor a perfect square trinomial,
4x² + 4x + 1
= 4x² + 2x + 2x + 1
= 2x (2x + 1) +1 (2x + 1)
= (2x + 1) (2x + 1)
