Vedic (GCD Polynomials)

G.C.D Polynomials by Vedic Math

Find G.C.D of P(x) & Q(x):

P(x) = 4x³ +13x²+19x+4
Q(x) = 2x³+5x²+5x -4

Vedic method:
1. Eliminate 4x³ in P(x):
P - 2Q = 3x² +9x+12

/3 => P-2Q = (x²+3x+4)

2. Q+P = 6x³+18x²+24x

/(6x) => Q+P = (x²+3x+4)

3. G.C.D. = (x²+3x+4)

P= (x² +3x+4).(ax+b) = 4x³ +13x²+19x+4
=> a=4, b=1
Similarly,
Q= (x² +3x+4).(2x+1) = 2x³+5x²+5x -4