Final answer:
The question involves dividing the polynomial (x^3 - 14x + 8) by (x + 4). It requires using long division or synthetic division and could be a step in simplifying an expression or solving a larger problem. Other hints in the question mention quadratic equations and negative exponents.
Step-by-step explanation:
The student provided an algebraic expression and requested help with dividing polynomials, specifically regarding the division (x3 - 14x + 8) ÷ (x + 4). To find the quotient, we need to apply long division or synthetic division for polynomials. The first step in this process is to divide the first term of the numerator by the first term of the denominator and then multiply the entire divisor by the obtained quotient term. This multiplication result is subtracted from the numerator, and the process is repeated with the new, simplified numerator until all terms have been divided. Polynomial division can often be made simpler with certain techniques such as completing the square or factoring, although this particular problem does not seem to require those methods. It's important to note within the question hints at other algebraic processes such as solving quadratic equations using the quadratic formula and understanding the concept of inverse operations indicated by negative exponents.