Final answer:
To find the remainder r(x) when dividing f(x) by d(x), we need to subtract the exponents of the exponential terms and perform polynomial division. However, the question lacks specific information about f(x) to calculate r(x). If d(x) = x + 1, we could potentially use the Remainder Theorem by substituting the zero of d(x) into f(x).
Step-by-step explanation:
To solve for the remainder term r(x) when dividing f(x) by d(x), we follow the division of exponentials rule. We first divide the digit terms, and then subtract the exponents for the exponential terms of the numerator by the corresponding terms of the denominator.
Following the question format, let's assume f(x) = x³ + 3x² + 3x + 3 and d(x) = x + 1. To find the remainder r(x), apply polynomial long division. However, since we only need the remainder and not the complete quotient, we can use synthetic division or directly apply the Remainder Theorem if d(x) is a factor of the form x - c.
Unfortunately, the question does not provide enough information to carry out the division process. We need a specific form for f(x) or additional context to calculate r(x). Assuming d(x) is x + 1, and if we had the specific f(x), we would substitute -1 (the zero of d(x)) into f(x) to obtain the remainder directly due to the Remainder Theorem.