Question

Solve the problem........ ​

Answer 1

$(x - 3)(6 {x}^{3} + 13 {x}^{2 } + x - 2) = 6 {x}^{4} - 5 {x}^{3} - 38 {x}^{2} - 5x + 6$

Answer 2

Answer:

6x^4 - 5x^3 - 38x^2 - 5x + 6

first we have to find a solution of this polynomial by hit and trial method. You may put x = 0,1,-1,2,-2 to find a solution. on putting x= -2, we find that value of the polynomial becomes zero, so (x+2) will be a factor of this polynomial.

(you need to show calculation for x = -2 which I skipped here)

6x^4 + 12x^3 - 17x^3 - 34x^2 - 4x^2 - 8x + 3x + 6

6x^3(x + 2) - 17x^2(x + 2) - 4x(x + 2) + 3(x + 2)

(x + 2) (6x^3 - 17x^2 - 4x + 3)

now we will repeat the process once again to find a solution of cubic equation

we find that x= 3 is a solution (you need to show the calculation which I am skipping)

hence (x - 3) will be a factor

(x+2)(6x^3 - 18x^2 + x^2 - 3x - x + 3)

(x + 2) (6x^2(x - 3) + x(x - 3) - 1(x - 3))

(x+2)(x - 3) (6x^2 + x - 1)

(x + 2) (x - 3) (6x^2 + 3x - 2x - 1)

(x + 2) (x - 3) (3x(2x + 1) - 1( 2x + 1))

(x + 2) (x - 3) (2x + 1) (3x - 1)

is the required factorisation..

(you can arrange the factors in any order)