Answer:
Option C - Perfect square trinomial.
Step-by-step explanation:
Given : Polynomial [tex]4x^2+12x+9[/tex]
To find : What pattern is represented by the polynomial?
Solution :
First we make the polynomial in factor form,
Polynomial [tex]4x^2+12x+9[/tex]
Since, it is not factor clearly so try to make the square.
Taking 4 common,
[tex]=4(x^2+3x+\frac{9}{4})[/tex]
Identifying the x and y terms in the identity,[tex](x+y)^2=x^2+y^2+2xy[/tex]
[tex]=4((x)^2+2\times x\times \frac{3}{2}+(\frac{3}{2})^2)[/tex]
Factor the perfect square trinomial,
[tex]=4(x+\frac{3}{2})^2)[/tex]
Therefore, The pattern polynomial represent is perfect square trinomial.
So, Option C is correct.
