1. **Problem:** Find the remainder when $y = x^4 + x^3 - 7x^2 + x + 3$ is divided by $x - 1$. 2. **Formula:** The Remainder Theorem states that the remainder of a polynomial $f(x)$ divided by $x - a$ is $f(a)$. 3. **Apply the theorem:** Here, $a = 1$, so calculate $f(1)$: $$f(1) = 1^4 + 1^3 - 7(1)^2 + 1 + 3 = 1 + 1 - 7 + 1 + 3$$ 4. **Simplify:** $$1 + 1 = 2$$ $$2 - 7 = -5$$ $$-5 + 1 = -4$$ $$-4 + 3 = -1$$ 5. **Result:** The remainder is $-1$, but the problem states the remainder is 4 when divided by $x - 1$. 6. **Check:** Since the problem states remainder 4, this suggests a discrepancy or a different polynomial or division. 7. **Conclusion:** Using the Remainder Theorem, the remainder when dividing $y$ by $x - 1$ is $-1$. **Final answer:** The remainder is $-1$.