With remainder theorem, how can I get the x in f(x)

A quotation from the text book:

In using Factor Theorem to find the factors, successive testings are tried until we find all the values of a(s) such that f(a)＝0. If, for example, we want to factorize

　　f(x)＝x³－8x²＋21x－18

the values worth testing should be the factors of 18, (i.e. ±1, ±2, ±3, ±6, ±9 and ±18).

Usually, we have to test only the small values, and, if all the coefficients of f(x) are positive, test only the negative values. If the coefficient of the term of the highest degree is not unity, we still have to try some more values.

However, if

　　f(x)＝8x³＋30x²－53x－15

the values worth testing is the fraction p/q where p must be a factor of 15 and q must be a factor of 8. (i.e. ±1, ±3, ±5, ±15, ±1/2, ±3/2, ±5/2, ±15/2, ±1/4, ±3/4, ±5/4, ±15/4, ±1/8, ±3/8, ±5/8, ±15/8). By substitution, we may find that f(－5), f(3/2) and f(－1/4) are all equal to zero.

try and error
即係試試下咋
不過, 都有 d 技巧
睇下常數項, -8
用佢既 因子 試下, 1, 2 等等 ....會快 d