Question

show that 2x-3 is a factor of x+2x^3-9x^2+12

Answer 1

you can find it yourself by putting values of x as 3/2

Answer 2

Step by step solution :

Step  1  :

Equation at the end of step  1  :

(((2 • (x3)) - 32x2) + x) + 12

Step  2  :

Equation at the end of step  2  :

((2x3 - 32x2) + x) + 12

Step  3  :

Checking for a perfect cube :

 3.1    2x3-9x2+x+12  is not a perfect cube 

Trying to factor by pulling out :

 3.2      Factoring:  2x3-9x2+x+12 

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  x+12 
Group 2:  2x3-9x2 

Pull out from each group separately :

Group 1:   (x+12) • (1)
Group 2:   (2x-9) • (x2)