(a) p(x) = (x – 1)2 (x + 1)2 (x2 + 1)
f(x) = x3 + x2 – x – 1
g(x) = x3 – x2 + x – 1
f(x) . g(x) = (x3 + x2 – x – 1) . (x3 – x2 + x – 1)
= x6 – x4 – x2 + 1
∴ p(x) = x6 – x4 – x2 + 1
= x4 (x2 – 1) – (x2 – 1) = (x2 – 1) (x4 – 1)
= (x – 1) (x + 1) [(x2)2 – 1]
= (x – 1) (x + 1) [(x2 – 1) (x2 + 1)]
= (x – 1) (x + 1) [(x – 1) (x + 1) (x2 + 1)]
= (x – 1)2 (x + 1)2 (x2 + 1).