this question does not make sense to me.

Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. then factor the trinomail.

X^2+21x+__

What is the constant term?

What is the factored for of the trinomial?

i just cant figure the constant

Take half of 21, and square it.

(21/2)^2
(x+21/2)^2

What you end up with will be

x^2 + 21x + 110.25 = (x + 10.5)^2

To determine the constant that needs to be added to make the trinomial a perfect square trinomial, we will follow these steps:

Step 1: Identify the first term of the trinomial, which is X^2.
Step 2: Identify the second term of the trinomial, which is 21x.
Step 3: Use the formula (a + b)^2 = a^2 + 2ab + b^2.
Step 4: Since the first term is X^2, we have (X + b)^2 = X^2 + 2Xb + b^2.
Step 5: Match the second term of the trinomial with 2Xb from the formula. In this case, b = 21/2.
Step 6: Square the value of b to get b^2. In this case, (21/2)^2 = 441/4.

Now that we have determined the constant term, which is 441/4, we can write the trinomial as a perfect square:

X^2 + 21x + 441/4

To factor this trinomial, we can rewrite it as a perfect square:

(X + 21/2)^2

Therefore, the constant term is 441/4, and the factored form of the trinomial is (X + 21/2)^2.