Question

f(x)= x^3 - 2x + 4
If f(x)=0, the real value of x= ?

I know I just need to factorize it, but I don't know how to factorize x^3 equations. Can anyone please explain to me the best/easiest way to factorize this? Thanks in advance!

Answer 1

set to zero then solve for x

Answer 2

f(x) = x^3 -2x + 4
y = x^3 -2x + 4
y = (x+2) (x^2-2x+2)

Answer 3

Can you tell me how you factorize it (like how you know that one of the roots is x+2)?

Answer 4

In fact the above is not correctly factored. Check by multiplying.

Answer 5

No, it's already correct (I checked it 3 times).

Answer 6

Okay it is correct factored. (spot on my screen made a - look like a +)

Answer 7

Okay it is correct factored. (spot on my screen made a - look like a +)

Answer 8

Can you explain to me how to factorize it?

Answer 9

Actually, there is not a general, no-fail method for factoring a cubic. However the last term (+4) seems to indicate there could be two factors end in 2 (either both + or both -) or possibly ending 1 and 4 (both positive or both negative). Since the coefficient on the cubed fact is 1, it is good to suspect that the coefficient on x in the factors is likely to be 1. Then you just try out some factors of the form x +/- n where n is 2, 1, 4. If there is not one factor with the first power of x, there will not be 2 or 3.

Answer 10

I see. Okay, then. Thank you for the explanation!