Question

разложить на множители

$126x^3+3x^2+3x+1$

Answer 1

$126x^3+3x^2+3x+1=125x^3+x^3+3x^2+3x+1=125x^3+(x+1)^3$=$(5x)^3+(x+1)^3=(5x+x+1)(25x^2-5x(x+1)+(x+1)^2)=$$(6x+1)(25x^2-5x^2-5x+x^2+2x+1)=(6x+1)(21x^2-3x+1)$