1. The problem is to find the remainder when one number or polynomial is divided by another. 2. For integers, use the division algorithm: if you divide $a$ by $b$, the remainder $r$ satisfies $a = bq + r$ where $0 \leq r < b$. 3. For polynomials, use polynomial long division or synthetic division to divide the dividend by the divisor. 4. The remainder is the polynomial left after subtracting the divisor times the quotient from the dividend. 5. Example: Find the remainder when $x^3 + 2x^2 + 4$ is divided by $x - 1$. 6. Using synthetic division: write coefficients $[1, 2, 0, 4]$ (note the missing $x$ term has coefficient 0). 7. Bring down 1, multiply by 1 (root of divisor), add to next coefficient: $1 \times 1 + 2 = 3$. 8. Repeat: $3 \times 1 + 0 = 3$, then $3 \times 1 + 4 = 7$. 9. The last number, 7, is the remainder. 10. So, the remainder when dividing $x^3 + 2x^2 + 4$ by $x - 1$ is $7$.