Final answer:
The quotient of the division of 5x^4 - 3x^2 by x^3 - x^2 is 5x, and the remainder is -3x^2.
Step-by-step explanation:
The question asks to find the quotient and remainder when 5x^4 - 3x^2 is divided by x^3 - x^2. To solve this, we perform polynomial long division. We divide 5x^4 by x^3 to get the first term of the quotient, which is 5x.
Multiplying 5x by x^3 - x^2 and subtracting it from 5x^4 - 3x^2 gives a remainder of −3x^2. So, the complete division is 5x^4 - 3x^2 = (5x)(x^3 - x^2) −3x^2. Therefore, the correct answer is option C: Quotient is 5x and Remainder is −3x^2.