Question

What number should be added to the expression x2+12x to change it into a perfect square trinomial?

6
12
18
36

Answer 1

The answer is 36. This is because both x2 and 36 are square numbers, and 12x is twice the product of x and 6. I hope this helps!

Answer 2

Fourth option is correct. We have to add 36 to change the given expression into a perfect square trinomial.

Explanation:

The perfect square trinomial is

`(a+b)^2=a^2+2ab+b^2`

The given expression is

`x^2+12x` .... (1)

If an expression is defined as

`ax^2+bx` ..... (2)

To change it into a perfect square trinomial we have to add
`((-b)/(2a))^2`.

On comparing (1) and (2), we get

`a=1`

`b=12`

To change the given expression into a perfect square trinomial we have to add

`((-b)/(2a))^2=((-12)/(2(1)))^2=36`

`x^2+12x+36=(x+6)^2`

Therefore to change the given expression into a perfect square trinomial we have to add 36 in the given expression.