Divide 2x4 - 9x3 + 5x2 + 3x - 8 by x2 - 4x +1 and verify the division algorithm.
Division algorithm:
If p(x) and g(x) are two polynomials such that degree of p(x) ≥ degree of g(x) and g(x ) ≠ 0, then p(x) = g(x) × q(x) + r(x), where q(x) and r(x) are quotient and remainder when p(x) is divided by g(x).
∴ Quotient q(x) = 2x2 – x – 1 and remainder r(x) = – 7
Verification:
