Factor compeletly and find all the zeros for these twp polyn

Factor compeletly and find all the zeros for these twp polynomial.

1- F(x) = 3x⁴-5x³-9x²+40x-12

2- G(x) = 3x³-5x²-8x-2

with the steps please.

1) f(x) = 3x^4 - 5x^3 - 9x^2 + 40x - 12

setting the equation equal to 0 to find the zeros

3x^4 - 5x^3 - 9x^2 + 40x - 12 = 0

solving teh equation for x

the function cannot be factored and it has no rational roots by rational root thorem

so applying quartic formula to find zeros of the function

we get two real zeros of the function

x1 = .3277

x2 = -2.3456

and two complex zeros

x3 = 1.84+1.345 i

x4 = 1.84 - 1.345 i

2) g(x) = 3x^3 - 5x^2 - 8x - 2

3x^3 - 5x^2 - 8x - 2 = 0

according to rational root test

possible rational roots are + - { 1 , 2 } / ( 1 , 3 }

+ - 1 , +- 1/3 , +- 2 , +- 2/3

at x = -1/3 g(x) becomes 0

hence one actual zero is x = -1/3

dividing g(x) by 3x +1

we get x^2 - 2x - 2

applying quadratic formula to find other two zeros

x = { -b +- b^2 - 4ac } / 2a

x = { 2 + - sqrt ( 4 + 4 } / 2 }

x 2 = 1 + sqrt 3

x3 = 1- sqrt 3

therefore,

3 zeros are

x1 = -1/3

x2 =1+ sqrt 3

x3 = 1 - sqrt 3