f(x) = X^3 + 2x^2 -4x -8: For zeroes of polynomial functions

This seems pretty simple but the book gave an unexpected answer


f(x)= x^3 +2x^2 -4x -8

0= the same as above

and

and

So that: +/- 4 and -2

This gives me (-4,0), (-2,0), and (4,0)

However the book gives the answer as {-2,2} without previously giving a similar answer to similar problems. Any guidance is much appreciated. Thanks.

By inspection f(2) = 2^3 + 2(4) - 4 - 8 = 0. Thus is a factor of f(x) by the factor theorem.

where A, B and C are constants to be found. You can either use long division or comparing coefficients to find them.

Once you have the quadratic you need to check if that will factor too

. So,



.

i.e. the solutions are (simple) and (double) .

Cool. Got it. It's always the dumb mistakes... Anyway, thanks to both of you very much.