Question

What is the quotient (3x3 + 10x2 + 10x + 4) ÷ (x + 2)?

a. 3x2 + 16x + 42
b. 3x2 + 4x + 2
c. 3x2 − 16x + 42
d. 3x2 − 4x + 2

Answer 1

the correct choice is B
3x^2 + 4x + 2

Answer 2

Option B is correct.

`3x^2+4x+2`.

Explanation:

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

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

`(3x^3+10x^2+10x+4)/(x+2)`

We can write the expression on the numerator as:

`3x^3+10x^2+10x+4=(3x^2+4x+2)(x+2)`

Hence,

`(3x^3+10x^2+10x+4)/(x+2)=((3x^2+4x+2)(x+2))/(x+2)`.

Hence,

`(3x^3+10x^2+10x+4)/(x+2)=3x^2+4x+2`.

Hence, option B is correct.

Hence, the quotient is:

`3x^2+4x+2`.