Question

(a) The L.C.M and H.C.F of two polynomials p(x) and g(x) are 24-1) and (x + 1)(x2 + 1)
respectively. If p(x) = x3 + x2 + x + 1, find q(x)​

Answer 1

Answer:

given :-

LCM is 24-1 = 23

HCF is (x+1)(x2+1) = x3 + x + x2 + 1

p(x) = x3 + x2 + x + 1

to find :-

q(x)= ?

p(x) × q(x) = LCM × HCF

x3 + x2 + x + 1 × q(x) = 23 × ( x3 + x2 + x + 1)

q(x) = 23 × ( x3 + x2 + x + 1) / ( x3 + x2 + x + 1)

q(x) = 23