Question

Разложить на множители 28х^3 +3х^2 +3х +1

Answer 1

27x^3 + 3x^2 + 3x + x^3 + 1= 3x*(x+1) + (x+1)*(x^2-x+1) + 27x^3=(x+1)*(3x+x^2-x+1) + 27x^3=(x+1)*(x^2+2x+1)+27x^3=(x+1)^3 + 27x^3=(x+1+3x)*((x+1)^2 -(x+1)*3x+9x^2)= (4x+1)*(x^2+2x+1-3x^2 -3x +9x^2)=(4x+1)*(7x^2-x+1)