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Given f(x) = 3x^3 - 2x^2 - 7x - 2.Given that x = 2 is a zero.
= > x - 2.
= > x - 2 is a factor.
Given that -1/3 is a zero
= > (x + 1/3) is a factor.
= > (3x + 1) is a factor.
Now,
= > (x - 2)(3x + 1) is a factor
= > 3x^2 + x - 6x - 2
= > 3x^2 - 5x - 2.
Hence, 3x^2 - 5x - 2 is a factor of f(x).
Now, by dividing f(x) by 3x^2 - 5x - 2.
x + 1
-------------------------------
3x^2 - 5x - 2) 3x^3 - 2x^2 - 7x - 2
3x^3 - 5x^2 - 2x
-------------------------------
3x^2 - 5x - 2
3x^2 - 5x - 2
------------------------------------
0
Now,
We find zeroes of x + 1.
= > x + 1 = 0
= > x = -1
Therefore Factorization of 3x^3 - 2x^2 - 7x - 2 = (x + 1)(x - 2)(3x + 1).
Hope this helps!
Refer to the attachment
Hope it helps you:-)