Please factorize x = t^3 − 13t^2 + 46t − 48. With full explanations.

Expert Answers
durbanville eNotes educator| Certified Educator

To factorize:


First arrange the expression so that it can simplify:

`= t^3 -13t^2+46t-27-21` (Note that -27-21=-48)

Now rearrange the order so that it can be factorized more readily:

`t^3 -27 -13t^2 +46t-21`

`` Now we can factorize:

`(t^3-27) - (13t^2 -46t +21)` (Note the negative (-) symbol)


Note we have a difference of two cubes (`t^3 and 3^3)`  and then a trinomial the factors of which (`1 times 13)` (first term) and    (`7 times 3 =21` )(third term) render a middle term of `-46`

Factorize by taking out the common factor:

`(t-3)[(t^2+3t +9) - (13t-7)(1)]`

Remove the brackets in side :


Simplify by adding like terms:


Factorize using the factors of the first term `(1 times 3)` and the factors of the third term which render the middle term of -10 (`2 times 8)` :



x= (t-3)(t-2)(t-8)


aruv | Student

Define function


Now ,find zeros of f(t) ,which possible may be `+-1,+-2,+-3,+-4,+-6,+-8,...`



Thus zero of f(t) is 2

By factor theorem , t-2  will be one factor of f(t)