SUMMARY
The problem involves finding the remainder when a polynomial f(x) is divided by x² - 4x + 3, given that the remainders for divisions by (x-1) and (x-3) are 2 and 4, respectively. The polynomial can be expressed as f(x) = (x-1)p(x) + 2 and f(x) = (x-3)q(x) + 4. By substituting x = 1 and x = 3 into the polynomial, two equations can be formed to solve for the coefficients a and b in the remainder expression ax + b.
PREREQUISITES
- Understanding of polynomial division
- Familiarity with the Remainder Theorem
- Knowledge of solving simultaneous equations
- Basic algebraic manipulation skills
NEXT STEPS
- Study the Remainder Theorem in detail
- Practice polynomial long division techniques
- Learn how to solve simultaneous equations effectively
- Explore the concept of polynomial remainders in higher degree polynomials
USEFUL FOR
Students studying algebra, particularly those tackling polynomial functions and remainders, as well as educators looking for examples of polynomial division applications.