can someone tell me if this problem is correct: Determine whether each of the following trinomials is perfect square. If it is factor the trinomial: x^2-24x+48
=(-24)^2-4(48)
To determine whether the trinomial x^2 - 24x + 48 is a perfect square, we need to compare it to the general form of a perfect square trinomial:
a^2 + 2ab + b^2
If it matches this form, then it is a perfect square trinomial.
Let's compare it to the general form:
x^2 - 24x + 48
= (x - 12)^2
Since the trinomial matches the pattern of a perfect square trinomial, we can conclude that it is a perfect square.
Now, let's factor the trinomial:
(x - 12)^2
When we expand this expression, we will get the original trinomial:
(x - 12)(x - 12) = x^2 - 24x + 144
So, the factored form of x^2 - 24x + 48 is (x - 12)^2.