There is a way to work it out with a pencil and paper, but that's too complicated
to try and explain with only text, like we have here.
I don't usually recommend this for things that can be done easily on paper ...
but for square roots, your best bet is to use a calculator.
The square root of 30 does not come out even. It starts out 5.477225...
and it keeps going and never ends.
The negative of 5.477225... is also a square root of 30. Every number has
two square roots ... the positive and negative of the same number.
The trial and error method is used to find an initial factor:
If we let f(x) = x³ - x² - 24x - 36 and all we have to do is sub' in values of x until
f(x) = 0, we can use this to find an initial factor by the factor theorem:
f(1) = (1)³ - (1)² - 24(1) - 36 = -60
f(2) = (2)³ - (2)² - 24(2) - 36 = -80
f(5) = (5)³ - (5)² - 24(5) - 36 = -56
*** f(6) = (6)³ - (6)² - 24(6) - 36 = 0 ***
f(6) = 0 so (x - 6) is a factor of f(x).
This means that: f(x) = x³ - x² - 24x - 36 = (x - 6)(ax² + bx + c).
To find a,b and c, use long division (or inspection) to divide x³ - x² - 24x - 36 by x - 6.
The other 2 factors of f(x) can then be found by factorizing the
ax² + bx + c quadratic the way you would with any other quadratic (i.e. by quadratic formula, CTS or inspection).
Multiply 2/10 by 3/1 and you should end up with 6/10
+ 19 on both sides, -19 becomes 0, 1 becomes 20 x=20
