Question

8x^4+24x^3-27x-81 what is the polynomial factor?

Answer 1

$8x^4+24x^3-27x-81=8x^3(x+3)-27(x+3)\\\\=(x+3)(8x^3-27)=(x+3)(2^3x^3-3^3)=(x+3)[(2x)^3-3^3]\\\\\text{use}\ a^3-b^3=(a-b)(a^2+ab+b^2)\\\\=(x+3)(2x-3)[(2x)^2+(2x)(3)+3^2]\\\\=\boxed{(x+3)(2x-3)(4x^2+6x+9)}$