How do you factorise the given polynomial x9-x6-x+1? - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

By grouping method
First factor two terms, factor

x^{6}

and two terms, factor the

- 1

that is

x^{6} (x^{3} - 1) - 1 (x^{3} - 1)

Factor out the common binomial factor

(x^{3} - 1)

so that

(x^{3} - 1) (x^{6} - 1)

at this point use “sum or difference of two cubes” forms and difference to two square

a^{3} - b^{3} = (a - b) (a^{2} + ab + b^{2})

a^{3} {+ b}^{3} = (a + b) (a^{2} - ab + b^{2})

a^{2} - b^{2} = (a - b) (a + b)

So that

(x - 1) (x^{2} + x + 1) (x^{3} - 1) (x^{3} + 1)

(x - 1) (x^{2} + x + 1) (x - 1) (x^{2} + x + 1) (x + 1) (x^{2} - x + 1)

(x - 1)^{2} {(x^{2} + x + 1)}^{2} (x + 1) (x^{2} - x + 1)

is the correct answer.

How do you factorise the given polynomial $x^{9} - x^{6} - x + 1$ ?