Question

Please Answer and get brainliest.....

Answer 1

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!

Answer 2

Hey!!!


Refer to the attachment


Hope it helps you:-)