Question

Which of the following values completes the square or creates a perfect square trinomial for x^2-12x+___

Answer 1

Answer:  The correct option is

(C) 36.

Step-by-step explanation:  We are given to select the value that completes the square or creates a perfect square trinomial for the following incomplete expression :

$E=x^2-12x+?$

We will be using the following square formula :

$a^2-2ab+b^2=(a-b)^2.$

Let the required value be represented by c.

We have

$E\\\\=x^2-12x+c\\\\=(x^2-2\times x\times 6+6^2)+c-6^2\\\\=(x-6)^2+c-36.$

So, for the given expression to be a perfect square trinomial, we must have

$c-36=0\\\\\Rightarrow c=36.$

Thus, the required value is 36.

Option (C) is CORRECT.

Answer 2

Answer:

So, 36 completes perfect square

Step-by-step explanation:

we are given

trinomial as

$x^2-12x+......$

we can square formula

$a^2-2ab+b^2=(a-b)$

we can see that middle term is 2ab

so, we will factor middle term in 2ab form

$12x=2\times x\times 6$

We can see that b is 6

so, if we could add 6^2 , then we will get perfect square

$x^2-12x+6^2......$

$x^2-12x+36......$

So, we should add 36

so, 36......Answer