I'm supposed to factor this:

Question

3z^2-17z+24

I used the quadratic equation, but I'm not sure if that's what I was supposed to use to get the answer. This is how I worked it...

-(-17)+/-sqrt(-17^2-4(3)(24)
---------------------------
2(3)
17+/-sqrt(289-288)
------------------
6
17 sqrt (1) = 17
----------- ----
6 6

is 17/6 correct?

Answer 1

the numbers are quite small, so a few trial and error runs would give you

(x-3)(3x-8)

your method should have given you
(17 +/- 1)/6 = 3 or 8/3

the root of 3 would have given the x-3 factor
the 8/3 would yield the (3x-8) factor

Answer 2

(3z- )(z - )
(3z- 4 )(z -6 ) no
(3z- 6)(z -4 )no
(3z- 8)(z - 3) YES

Answer 3

oh :( okay I definitely used the wrong method then. trial and error is a lot less steps than I used. thank you