Select the polynomial that is a perfect square trinomial.

9x^2 + 9x + 1
36b^2 − 24b + 8
16x^2 + 24x + 9
4a^2 − 10a + 25

the third one because the square root of the first number is 4x and the last number is 3. multiply these two numbers and then multiply that number by two, you get 24x. That is the middle number so the third option is your number

To determine if a polynomial is a perfect square trinomial, we need to identify if it can be factored as the square of a binomial.

In a perfect square trinomial, the first and last term must be perfect squares, while the middle term is twice the product of the square roots of the first and last term.

Let's analyze the given polynomials:

1) 9x^2 + 9x + 1
The first term is a perfect square (3x)^2, the middle term is 2(3x)(1) = 6x, which is not equal to 9x, and the last term is a perfect square (1)^2. Therefore, this polynomial is not a perfect square trinomial.

2) 36b^2 − 24b + 8
The first term is a perfect square (6b)^2, the middle term is 2(6b)(-2) = -24b, and the last term is a perfect square (2)^2. Therefore, this polynomial is not a perfect square trinomial.

3) 16x^2 + 24x + 9
The first term is a perfect square (4x)^2, the middle term is 2(4x)(3) = 24x, and the last term is a perfect square (3)^2. Therefore, this polynomial is a perfect square trinomial.

4) 4a^2 − 10a + 25
The first term is a perfect square (2a)^2, the middle term is 2(2a)(-5) = -20a, and the last term is a perfect square (5)^2. Therefore, this polynomial is not a perfect square trinomial.

From the given options, the polynomial that is a perfect square trinomial is 16x^2 + 24x + 9.