Question

if p (x) is a common multiple of degree 6 of the polynomials, f (x) = x³ + x² - x - 1 and g (x) = x³ - x² + x - 1, then p (x) is.
(a) 0
(b) x³ + x² - x - 1
(c) 1
(d) ( x - 1 )² ( x + 1)² ( x² + 1 )

Answer 1

Answer:

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).Read more on Sarthaks.com - https://www.sarthaks.com/1002615/if-p-x-is-a-common-multiple-of-degree-6-of-the-polynomials-f-x-x-3-x-2-x-1-and-g-x-x-3-x-2-x-1-then-which

Answer 2

Answer:

option 1 is the correct answer