Final answer:
The student needs to perform polynomial division of x³ + 3x² - 2x + 7 by x - 2 using either polynomial long division or synthetic division.
Step-by-step explanation:
The student is asking to evaluate a polynomial division where the polynomial x³ + 3x² - 2x + 7 is divided by x - 2. We can apply either polynomial long division or synthetic division to solve this.
Using polynomial long division, we divide each term of the polynomial by x - 2 starting from the highest degree term. Each time we divide, we multiply the result by x - 2 and subtract from the polynomial to get the remainder. We repeat the process until the terms left have a degree lower than that of x - 2, which is 1 in this case.
Alternatively, we can use synthetic division which is a simplified form of polynomial division when dividing by a linear term. It involves using the coefficients of the polynomial and the root of x - 2, which is 2, to systematically find the result and the remainder.