Answered

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 ??

Verified Answer :

Answer:

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

(
3a
−5)^2

Step-by-step explanation:

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.

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