Question

find the lcm of x3+x2+x+1 and x4-1​

Answer 1

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

and
x⁴ - 1
= (x²)² - (1)²
= (x² + 1) (x² - 1)
= (x² + 1) (x + 1) (x - 1)

Therefore,
LCM = (x² + 1) (x + 1) (x - 1)
= (x² + 1) (x² - 1)
= x⁴ - 1

HOPE IT'LL HELP...: )

Answer 2

Answer:

x⁴ - 1

Given:

2 equations:

x3+x2+x+1 and x4-1​

To find:

LCM of the above 2 equations

Solution:

x³ + x² + x + 1

x² ( x + 1) + 1 (x + 1)

(x² + 1) (x + 1)

x⁴ - 1

(x²)² - (1)²

(x² + 1) (x² - 1)

(x² + 1) (x + 1) (x - 1)

LCM = (x² + 1) (x + 1) (x - 1)

(x² + 1) (x² - 1)

x⁴ - 1

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