Question

x^5+x^4+x^3+x^2+x+1=0 factorise​

Answer 1

Answer:

Factoring: x5+x4+x3-x2+x-1

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: x3-x2

Group 2: x5+x4

Group 3: x-1

Pull out from each group separately :

Group 1: (x-1) • (x2)

Group 2: (x+1) • (x4)

Group 3: (x-1) • (1)

Looking for common sub-expressions :

Group 1: (x-1) • (x2)

Group 3: (x-1) • (1)

Group 2: (x+1) • (x4)

Adding (1) + (3): (x-1) • (x2+1)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.