Suppose \(P(x) \) is a polynomial satisfying \( P(0) = 1, P(1) = 2, P(2) = 5, P(3) = 10, P(4) = 17\). Find \( P(5)\). Hint: Consider the polynomial \( P(x) - x^2 - 1\).
Q42–Q43: Spotting that P(x)−f(x) has multiple roots is a classic RI/HCI technique. Q44–Q45: Use modular reduction of powers instead of brute-force expansion. Q47: Partial fractions leading to a telescoping sum is a common enrichment theme. Q48: Recognising a hidden polynomial pattern avoids solving a large system of equations.

Suppose \(P(x) \) is a polynomial satisfying \( P(0) = 1, P(1) = 2, P(2) = 5, P(3) = 10, P(4) = 17\).
Find \( P(5)\).
*Hint: Consider the polynomial \( P(x) - x^2 - 1\).*

Q42–Q43: Spotting that P(x)−f(x) has multiple roots is a classic RI/HCI technique.
Q44–Q45: Use modular reduction of powers instead of brute-force expansion.
Q47: Partial fractions leading to a telescoping sum is a common enrichment theme.
Q48: Recognising a hidden polynomial pattern avoids solving a large system of equations.

Polynomials, Cubic Equations and Partial Fractions

Polynomials, Cubic Equations and Partial Fractions