SUMMARY
The problem involves finding the value of k in the polynomial 4x² + 9x + k when divided by x - 1, given that the remainder is 3. To solve for k, one can utilize the Remainder Theorem, which states that the remainder of a polynomial P(x) divided by x - a is P(a). By substituting x = 1 into the polynomial, the equation becomes 4(1)² + 9(1) + k = 3. Solving this yields k = -10.
PREREQUISITES
- Understanding of polynomial functions
- Familiarity with the Remainder Theorem
- Basic algebraic manipulation skills
- Knowledge of polynomial division concepts
NEXT STEPS
- Study the Remainder Theorem in depth
- Practice polynomial division techniques
- Explore applications of polynomial functions in calculus
- Learn about synthetic division as an alternative method
USEFUL FOR
Students in algebra or calculus courses, educators teaching polynomial functions, and anyone looking to strengthen their understanding of polynomial division and the Remainder Theorem.