Final answer:
The correct combination of the given expressions (-3x + 3x^2) + (x^2 - x + 1) results in 4x^2 - 4x + 1. The use of 'quotient' seems to be a mistake as it suggests division, not addition or subtraction. None of the given options match this simplified expression.
Step-by-step explanation:
The student's question asks for the quotient of the expressions (-3x + 3x^2) + (x^2 - x + 1). To simplify this, we combine like terms.
First, let's add like terms:
- (3x^2 + x^2) = 4x^2,
- (-3x - x) = -4x,
- (1 + 0) = 1.
Combining them gives us the simplified expression 4x^2 - 4x + 1.
However, the error in the usage of the word 'quotient' should be noted. A quotient typically results from division, not addition or subtraction. In this case, we are simply combining like terms, not actually dividing. Hence, among the given options, none matches our answer, indicating that either the options are incorrect, or the problem has been misunderstood.