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).
1 1/2 - 2 1/2 is 3/2:5/2 or a 3:5 ratio
2 2/5 - 4 is 12/5:20/5 or a 3:5 ratio
3 3/4 - 6 1/4 is 15/4:25/4 or a 3:5 ratio
4 - 6 2/3 is 12/3:20/3 or a 3:5 ratio
1.2- 2 if divided by .4 is a 3:5 ratio
1.8-3 if divided by .6 is a 3:5 ratio
the unit rate is 3:5
Since all units are 3:5 it is proportional
(25 -21)/(28 -20) = 4/8 = 1/2
Your probability is 1/2.
204204 - 16 = 204188
204188 / 4 = 51,047
width = 51,047
length = 51,055
