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

Answer:

Option C - Perfect square trinomial.

Step-by-step 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,

$=4(x^2+3x+\frac{9}{4})$

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

$=4((x)^2+2\times x\times \frac{3}{2}+(\frac{3}{2})^2)$

Factor the perfect square trinomial,

$=4(x+\frac{3}{2})^2)$  

Therefore, The pattern polynomial represent is perfect square trinomial.

So, Option C is correct.