Question

how would you factorise x^4 -x = 0
x(x^3 -1)=0
x(x-1)(........?.)=0
i cant seem to go further than that, wouldnt the blank be x^2 +1

Answer 1

Thank you for showing what you've done so far. You're exceptional!

x(x^3 -1)=0
x(x-1)(........?.)=0

are both fine.

x^3-1 = x^3 - 1^3 is "the difference of two cubes."

Where have you seen that name before? Hint: Look up "special products and factors."

Answer 2

my textbook says x(x-1)(x^2 +x +1) =0 i dont get how you get (x^2 + x +1)