What is the quotient? x + 1)3x2 − 2x + 7

We are dividing  by (x+1).

According to the "Division algorithm":

P(x)=D(x)*Q(x)+R(x), 

where P(x) is the dividend polynomial, D(x) is the divisor polynomial, Q(x) is the quotient polynomial and R(x) the remainder which must be of smaller degree than the divisor.

so


R(x)=c, a constant, because the divisor is a linear.

also notice that Q(x) must be a linear of the form 3x+a:



comparing the coefficients, we have:

-2=a+3                and           7=a+c

a=-5,           then     7=-5+c, so c=-12

the quotient is 3x-5