Final answer:
To factor the given expression, we identify the greatest common factor (GCF), which is 10b^5a. After dividing each term by 10b^5a, option (c) is the closest to a complete factoring: 10b^5a(-9b^3 + 6c^3 + 9b^2a + bc^2). The unknown powers in the question prohibit a fully accurate completion.
Step-by-step explanation:
To factor the expression given, we need to find the greatest common factor (GCF) of all terms. The terms are -90b^8a, 60b^5ac^3, 90b^?a?, and 10b^6c^2. First, we identify the GCF for the numerical coefficients, which is 10. Next, we find the lowest power of b that appears in all terms, which is b^5. The variable a also appears in all terms, but since the powers of a aren't provided for all terms, we will assume the lowest power is a, as it appears in the term with the unknown exponents.
Therefore, the GCF of the given expression is 10b^5a. After dividing each term by the GCF, the factored expression is:
10b^5a(-9b^3 + 6c^3 + 9b^?a? + b^2c^2)
Due to the unknown powers of b and a in the third term, we cannot complete the factoring without that information. Thus, the answer closest to a complete factoring, given the information provided, would be option (c).