## Respuesta :

**Answer:**

Option B is correct.

[tex]3x^2+4x+2[/tex].

**Step-by-step explanation:**

We are asked to find the quotient obtained by dividing the expression [tex](3x^3+10x^2+10x+4)[/tex] by the expression [tex](x+2)[/tex]

We can also write this expression as i.e. we are asked to find the value of the expression:

[tex]\dfrac{3x^3+10x^2+10x+4}{x+2}[/tex]

We can write the expression on the numerator as:

[tex]3x^3+10x^2+10x+4=(3x^2+4x+2)(x+2)[/tex]

Hence,

[tex]\dfrac{3x^3+10x^2+10x+4}{x+2}=\dfrac{(3x^2+4x+2)(x+2)}{x+2}[/tex].

Hence,

[tex]\dfrac{3x^3+10x^2+10x+4}{x+2}=3x^2+4x+2[/tex].

**Hence, option B is correct.**

**Hence, the quotient is:**

**[tex]3x^2+4x+2[/tex].**