we have
6x^3+ 23x^2 - 6x -8 : (3x-2)
step 1
Verify if (3x-2) represents a factor
If (3x-2) is a factor
then
3x-2=0 ------> x=2/3
Substitute the value of x=2/3 in the given expression
6(2/3)^3+23(2/3)^2-6(2/3)-8
6(8/27)+23(4/9)-4-8
(16/9)+(92/9)-12
12-12=0
that means
(3x-2) is a zero of the given function
therefore
