Determine which polynomial is a perfect square trinomial.
49x2 − 28x + 16
9a2 − 30a + 25
25b2 − 45b − 81
16x2 − 24x − 9
is it b pls help me
3 times 5 is 15 and 15+15 = 30 so try the second one
(3a-5)((3a-5)
To determine which polynomial is a perfect square trinomial, we need to check if it can be factored into the square of a binomial.
Let's check each polynomial:
1) 49x^2 - 28x + 16:
This trinomial cannot be factored into the square of a binomial since 49x^2, 16, and 28x are not perfect square terms. Therefore, it is not a perfect square trinomial.
2) 9a^2 - 30a + 25:
This trinomial can be factored into (3a - 5)^2, which is the square of the binomial (3a - 5). Therefore, it is a perfect square trinomial.
3) 25b^2 - 45b - 81:
This trinomial cannot be factored into the square of a binomial since 25b^2, 45b, and 81 are not perfect square terms. Therefore, it is not a perfect square trinomial.
4) 16x^2 - 24x - 9:
This trinomial cannot be factored into the square of a binomial since 16x^2, 24x, and 9 are not perfect square terms. Therefore, it is not a perfect square trinomial.
Therefore, the correct answer is:
b) 9a^2 - 30a + 25
To determine whether a polynomial is a perfect square trinomial, we need to check if it can be factored as the square of a binomial.
The general form of a perfect square trinomial is (a ± b)^2, where a and b are constants.
Let's check each option:
a) 49x^2 - 28x + 16
This is not a perfect square trinomial because the coefficient of the linear term (-28x) is not twice the product of the square root of the leading coefficient (49x^2) and the square root of the constant term (16).
b) 9a^2 - 30a + 25
This is a perfect square trinomial because it can be factored as (3a - 5)^2. The square root of 9a^2 is 3a, and the square root of 25 is 5.
c) 25b^2 - 45b - 81
This is not a perfect square trinomial because the coefficient of the linear term (-45b) is not twice the product of the square root of the leading coefficient (25b^2) and the square root of the constant term (-81).
d) 16x^2 - 24x - 9
This is not a perfect square trinomial because the coefficient of the linear term (-24x) is not twice the product of the square root of the leading coefficient (16x^2) and the square root of the constant term (-9).
From the given options, the only perfect square trinomial is b) 9a^2 - 30a + 25.
Therefore, your answer is correct.