Answer:
f(x) = (x + 1)(2x - 3)(3x - 5)
Explanation:
The given function is f(x) = 6x³- 13x²- 4x + 1
If we substitute x = -1 then we get f(-1) = 0. Therefore (x + 1) is a zero factor.
Now we will use synthetic division to get the polynomial factorized.
(-1) | 6 -13 -4 15
___-6__19_-15_
6 -19 15 0
Now we get the polynomial as (x + 1)(6x²- 19x + 15)
Now we factorize (6x² - 19x + 15)
6x² - 19x + 15 = 6x² - 10x - 9x + 15
= 2x(3x - 5) - 3(3x - 5)
= (2x - 3)(3x - 5)
Finally we get the expression in the factored form as (x + 1)(2x - 3)(3x - 5).