Question

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

49x2 − 28x + 16
9a2 − 30a + 25
25b2 − 45b − 81
16x2 − 24x − 9
I know how to slove but isn't b and d perfect square trinomials ??

Answer 1

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

( 3a −5)^2

Explanation:

Answer 2

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

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.