Final answer:
To find the remainder when (9x + 8x² + 7x³ + ... + x) is divided by (x+1), substitute (-1) for x in the polynomial and evaluate.
Step-by-step explanation:
To find the remainder when (9x + 8x² + 7x³ + ... + x) is divided by (x+1), we can use the Remainder Theorem. According to the Remainder Theorem, if a polynomial f(x) is divided by (x - a), the remainder is equal to f(a).
In this case, we can substitute (-1) for x in the given polynomial to find the remainder. So, the remainder when (9x + 8x² + 7x³ + ... + x) is divided by (x+1) is equal to f(-1), where f(x) = 9x + 8x² + 7x³ + ... + x.
Plugging in (-1) for x, we get f(-1) = 9(-1) + 8(-1)² + 7(-1)³ + ... + (-1) = -9 + 8 - 7 + ... - 1.