Gee, greensnake, you should have a little clue or you should not have been given this assignment.

1) It's "factor". "Factories" is something else all together and "factorize" is quite excessive.

2) A "zeropoint" is likely to be a value of the variable that makes the entire expression equal to zero (0).

For a), try x = 1 x^2 - 4x + 3 ==> 1^2 - 4(1) + 3 = 1 - 4 + 3 = 0!!

For general factoring, WRITE DOWN what you know.

For a) x^2 - 4x + 3 = (x - ___)(x - ___) This much can be seen immediately, since whatever the two missing numbers are must sum to -4 and multiply to +3. (If you do not know why this is, you need a much more fundamental review.) You just have to find the missing numbers with those properties. Generally, a nice search from the factors of 3 is a good place to get started. In this case, just 1 and 3 do the trick and we have:

x^2 - 4x + 3 = (x - 1)(x - 3)

From the factored form, the "zeropoints" are obvious. x = 1 and x = 3.

Okay, you do the next one.