Question

the lcm of x3+1 and x2-x+1 is​

Answer 1

Lcm is x^3 + 1
Reason x^3+1=(x+1)(x^2-x+1)

Answer 2

Answer:

LCM of x³+1 and x²-x+1 = x³+1

Step-by-step explanation:

Given expressions are x³+1 and x²-x+1

To find,

The LCM of the given two expressions

Recall the formula

a³ + b³ = (a + b) (a² – ab + b²) ---------------(1)

Solution

Given expressions are x³+1 and x²-x+1

Factorize x³+1 using a³ + b³ we get

x³+1 = (x+1)(x²-x+1)

LCM of x³+1 and x²-x+1 = LCM of  (x+1)(x²-x+1) and x²-x+1

=  (x+1)(x²-x+1)

=x³+1

∴LCM of x³+1 and x²-x+1 = x³+1

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