What is the completely factored form of f(x) = 6x3 – 13x2 – 4x + 15?

f(x) = (x + 1)(2x - 3)(3x - 5)

Step-by-step 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).

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step-by-step explanation: