Question

разложить на множители, комбинируя различные способы

m^3 + 10m + 5m^2 + 8

x^3 + 10x^2 - 20x - 8

Answer 1

1) (M^3 + 8) + (10 M + 5M^2) = (M + 2)(M^2 - 2M + 4) + 5M(2 +M) = (M +2)(M^2 - 2M +4 + 2 +M) =

= (M + 2) (M^2 -M +6)

2) X^3 + 10X^2 - 20X - 8 = (X^3 - 8) + (10X^2 - 20X) = (X -2)(X^2 +2X +4)  + 10X(X - 2) = (X -2)(X^2 + 2X + 4 + X - 2) = (X -2)( X^2 + 3X + 2) = (X-2)(X+1)(X+2)