Question

Determine which polynomial is a perfect square trinomial. (5 points)

Answer 1

Answer:

It is 9a2 − 30a + 25 The other answer is a prime number.

( 3a −5)^2

Step-by-step explanation:

Answer 2

Answer:

Option 2 - $9a^2-30a + 25=(3a-5)^2$

Step-by-step explanation:

To find : Determine which polynomial is a perfect square trinomial?

Solution :

The perfect square trinomials are of the form :

$A^2\pm 2AB+b^2=(A\pm B)^2$

Now, We check one by one which form make this satisfied.

1) $49x^2-28x + 16$

We can re-write as

In this A=7x and B=4

Putting in formula,

$(7x)^2-2(7x)(4)+(4)^2=49x^2-56x+16$

So, The above equation will not form a trinomial.

2) $9a^2-30a + 25$

We can re-write as

In this A=3a and B=5

Putting in formula,

$(3a)^2-2(3a)(5)+(5)^2=9a^2-30a+25=(3a-5)^2$

So, The above equation will satisfy the form it is a trinomial.

3) $25b^2-45b-81$

We can re-write it trinomial form due to negative sign.

So, The above equation will not form a trinomial.

4) $16x^2-24x-9$

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.