Question

How do you factor `x^6-7x^3-8`?

Answer 1

Like this,

`x^6-7x^3-8 -= (x^3)^2 -7(x^3) -8 -= (x^3-8)(x^3+1) -= (x^3-(2)^3)(x^3+(1)^3)`

Recall that, `a^3+b^3=(a+b)(a^2-ab+b^2)` and `a^3-b^3=(a-b)(a^2+ab+b^2)`

`=> (x-2)(x^2+2x+4)(x+1)(x^2-x+1)`