Respuesta :
Answer:
It is 9a2 − 30a + 25 The other answer is a prime number.
( 3a −5)^2
Step-by-step explanation:
Answer:
Option 2 - [tex]9a^2-30a + 25=(3a-5)^2[/tex]
Step-by-step explanation:
To find : Determine which polynomial is a perfect square trinomial?
Solution :
The perfect square trinomials are of the form :
[tex]A^2\pm 2AB+b^2=(A\pm B)^2[/tex]
Now, We check one by one which form make this satisfied.
1) [tex]49x^2-28x + 16[/tex]
We can re-write as
In this A=7x and B=4
Putting in formula,
[tex](7x)^2-2(7x)(4)+(4)^2=49x^2-56x+16[/tex]
So, The above equation will not form a trinomial.
2) [tex]9a^2-30a + 25[/tex]
We can re-write as
In this A=3a and B=5
Putting in formula,
[tex](3a)^2-2(3a)(5)+(5)^2=9a^2-30a+25=(3a-5)^2[/tex]
So, The above equation will satisfy the form it is a trinomial.
3) [tex]25b^2-45b-81[/tex]
We can re-write it trinomial form due to negative sign.
So, The above equation will not form a trinomial.
4) [tex]16x^2-24x-9[/tex]
We can re-write it trinomial form due to negative sign.
So, The above equation will not form a trinomial.
Therefore, Option 2 is the only which make a perfect square trinomial.
