Question

What pattern is represented by the polynomial ? 4x^2+12x+9 A. difference of two squares B. general trinomial C. perfect square trinomial D. prime trinomial

Answer 1

Option C - Perfect square trinomial.

Explanation:

Given : Polynomial
`4x^2+12x+9`

To find : What pattern is represented by the polynomial?

Solution :

First we make the polynomial in factor form,

Polynomial
`4x^2+12x+9`

Since, it is not factor clearly so try to make the square.

Taking 4 common,

`=4(x^2+3x+(9)/(4))`

Identifying the x and y terms in the identity,
`(x+y)^2=x^2+y^2+2xy`

`=4((x)^2+2* x* (3)/(2)+((3)/(2))^2)`

Factor the perfect square trinomial,

`=4(x+(3)/(2))^2)`

Therefore, The pattern polynomial represent is perfect square trinomial.

So, Option C is correct.