The divisor of the expression $x(x^2-1)(3x+2)$ for every integer x is-

Explanation

Given that, the expression is F(x) = $x(x^2 - 1)(3x+2)$ For each integer- On putting, x = 1, 2, 3, 4, 5....... $x = 1, F(1) = 1(1^2-1) (3\times1 + 2) = 0 = 24 \times 0$ $x = 2, F(2) = 2(2^2-1).(3\times2+2) = 2\times3\times8 = 24\times2$ $x = 3, F(3) = 3(3^2-1).(3\times3+2) =3\times11\times8 = 24\times11$ $x = 4, F(4) = 4(4^2-1).(3\times4+2) = 4\times15\times14 = 24\times35$ $x = 5, F(5) = 5(5^2-1).(3\times5+2) =5\times24\times17 = 24\times85$ Thus, the divisor of the given expression $x.(x^2-1).(3x+2)$ for each integer is x = 24