The dividend is 3x² - 2x + 1.

The dividend is a polynomial of degree 2, which means it is a quadratic polynomial. The dividend is given as 3x² - 2x + 1.

The answer is: (x-1)²

A step-by-step solution:

Factor the dividend.

$$3x^2-2x=(3x)(x)-2(x)=(x-1)(3x)$$

Set the dividend equal to the product of the divisor and the quotient plus the remainder.

$$(x-1)(3x)=(x+2)(Q)+R$$

Distribute and combine like terms.

$$3x^2-2x=(x+2)Q+R$$
$$3x^2-2x=xQ+2Q+R$$

Equate the coefficients of like terms.

Coefficient of x²: 3 = Q
Coefficient of x: -2 = Q - 2
Constant: 0 = R

Solve for Q.

$$3=Q$$
$$-2=Q-2$$

$$-2+2=Q-2+2$$

$$0=Q$$

Substitute 0 for Q and simplify.

$$(x-1)(3x)=(x+2)(0)+R$$
$$(x-1)(3x)=R$$

Therefore, the remainder is R = (x-1)(3x).