1. **State the problem:** Find the remainder when the polynomial $f(x) = 7x^{16} - 8x^{11} + x - 3$ is divided by $x - 1$. 2. **Recall the Remainder Theorem:** When a polynomial $f(x)$ is divided by $x - a$, the remainder is $f(a)$. 3. **Apply the theorem:** Here, $a = 1$, so the remainder is $f(1)$. 4. **Evaluate $f(1)$:** $$f(1) = 7(1)^{16} - 8(1)^{11} + 1 - 3 = 7 - 8 + 1 - 3$$ 5. **Simplify:** $$7 - 8 + 1 - 3 = (7 - 8) + (1 - 3) = -1 - 2 = -3$$ **Final answer:** The remainder is $-3$.