Determine one solution using the factor theorem and then find the remaining solutions using synthetic division

Question

4x³+x²-27x+18=0 

 

determine one solution using the factor theorm and then find the remaining solutions using synthetic division of the equation. 

Answer 1

4x³+x²-27x+18=0...Eq1

 

Try putting x=some numbers. You will get a zero for  atleast for one

of the value.

put x=-3 in Eq1

 

-108+9+81+18=0

 

so x=-3 is a solution.

x=-3

∴x+3=0

so, x+3 is a factor of  the Eq1

 

let's apply synthetic division.

 

  -3 | 4   1     -27   18

      |

      |      -12   33    -18

       ---------------------

        4   -11   6        0

 

so we have 4x²-11x+6=0......Eq2  is another solution.

 solving equation2 will give us the rest of the solutions.

 

4x²-11x+6=0

∴4x²-8x-3x+6=0

∴4x(x-2)-3(x-2)=0

∴(4x-3)(x-2)=0

∴4x-3=0     and    x-2=0

∴x=3/4       and x=2

 

so we now have x=-3,x=3/4 and x=2 are the solutions of the Eq1 ANS

 

or 4x³+x²-27x+18=(4x-3)(x-2)(x+3)....ANS  

 

Try putting x=2 and x=3/4 in Eq1 to check if you get 0 or not.