Question

Factor (x-1)^3 (4x-9) - (16x+9) (x+1)^2 ? Please explain steps, I'm stuck !

Answer 1

$(x-1)^3 (4x-9) - (16x+9) (x+1)^2$

$= (x^3-3x^2+3x-1) (4x-9) - (16x+9) (x^2+2x+1)$

$= (4x^4-12x^3+12x^2-4x-9x^3-27x^2-27x+9)-(16x^3+32x^2+16x+9x^2+18x+9)$

$= (4x^4-21x^3+39x^2-31x+9)-16x^3-32x^2-16x-9x^2-18x-9$

$= 4x^4-21x^3+39x^2-31x+9-16x^3-32x^2-16x-9x^2-18x-9$

$= 4x^4-37x^3-2x^2-65x$

$= x(4x^3-37x^2-2x-65)$

hence final factor is $x(4x^3-37x^2-2x-65)$