Final answer:
A perfect square trinomial is a trinomial that can be factored into two identical binomials. Option A (X^2-9) is a perfect square trinomial.
Step-by-step explanation:
A perfect square trinomial is a trinomial that can be factored into two identical binomials. One of the ways to determine if a trinomial is a perfect square is to check if the first and last terms are perfect squares, and if the middle term is twice the product of the square root of the first term and the square root of the last term. Let's check the options given:
A. X2-9: The first term, X2, is a perfect square. The last term, -9, is also a perfect square. The middle term, 0X, is twice the product of the square root of 1 (X) and the square root of 9 (3): 2(X)(3) = 6X. Therefore, this is a perfect square trinomial.
B. X2-100: The first term, X2, is a perfect square. The last term, -100, is also a perfect square. The middle term, 0X, is not twice the product of the square root of 1 (X) and the square root of 100 (10): 2(X)(10) = 20X. Therefore, this is not a perfect square trinomial.
Based on the above analysis, option A (X2-9) is a perfect square trinomial.
Learn more about Perfect Square Trinomials