Question

what is the factor of a^3 - 2a + 4?
please help me guys. :(

Answer 1

Hint:
A cubic has to have at least one zero.
If the expression has rational factors, there would be at least one linear factor fininishing in 1,2,4 or -1,-2,-4, since the coefficient of a^3 is 1.

For f(a)=a^3 - 2a + 4
So check f(1),f(2),... and which factor is in f(a). Do a long division and try to factor the remaining quadratic.

Answer 2

Sorry, the last paragraph is not clear.
If f(a0)=0, then (x-a0) is a factor of f(a). So check and see which of f(1),f(2)...=0 and hence find a rational factor of f(a).
If f(-1)=0, then (a+1) is a factor.
Do a long division and factor the remaining quadratic.