MAHARASHTRA Class 9: Remainder and Factor Theorem Videos | Factorization of polynomials using Factor Theorem

A polynomial of degree 1 is said to be a linear polynomial.

∴ y + 5 is a linear polynomial.

(x + a) is a factor of f(x).

∴ f(−a) = 0

∴ (−a)⁴ - a²(−a)² + 3(−a) - a = 0

∴ a⁴ − a⁴ - 4a = 0

∴ a = 0

P(x) = 2x³ - 9x² + x + 12

∴ P(−1) = 2(−1)³ - 9(−1)² + (−1) + 12 = 0