Solve This Equation?

Question

Solve the equation 6x^3 - 17x^2 - 5x + 6 = 0

(x-3) is a factor - cannot solve other part

please can you explain how you do this in detail as i missed this lesson and am having some trouble doing the homework!

Note: 6x^3 MEANS 6xCubed (6x to the power of (^) 3)

thanks

Answer 1

6x^2(x-3)+x(x-3)-2(x-3)=0
=>(x-3)(6x^2+x-2)=0
=>(x-3)(6x^2+4x-3x-2)=0
=>(x-3){2x(3x+2)-1(3x+2)}=0
=>(x-3)(3x+2)(2x-1)=0
Therefore x-3,3x+2 or 2x-1 is equal to zero
Therefore x=3,-2/3 or 1/2 ans.

Answer 2

You are right, x-3 is a factor of the left-hand side.
By long division or synthetic division, the other
factor is 6x² + x -2.
Now set this factor to 0 and solve
6x² + x -2 = 0
(3x+2)(2x-1)=0
Set each of these factors to 0 and solve.
We get x = -2/3 and x = 1/2
as the other 2 roots.

Answer 3

cube 6 and get 6 x 6 x 6 or 36 x 6 which is 216

then, square 17 which is 17 x 17 or 289

then this is 216 - 289 -5x +6 = 0

-73 -5x +6 = 0

-73 + 6 = 0 + 5x (you add 5x to each side)

-67 = 5x

divide both sides by 5

- 67/5 = 5x/5

-13.4 = x

so x = negative 13.4

Answer 4

have no clu3 but who gives a crap bout math