In the equation y=x3-x2-14x+24   a) find one zero b) synthetically divide and factor to find the remaining rwo zeros.

Expert Answers
hala718 eNotes educator| Certified Educator

`y= x^3 -x^2 -14x + 24 `

Let x= 2 ==> 8-4 -28 +24 = 0

Then (x-2) is a factor of y.

Now we will divide y by (x-2).

               

                `x^2+x -12`

               -----------------------    

   `x-2`       `x^3 -x^2 -14x +24`

                `x^3 -2x^2`

              -------------------------

                   `x^2 -14x + 24`

                    `x^2 -2x `

                ---------------------

                         `-12x + 24`

                         `-12x + 24 `

 

`==> y= (x-2)(x^2+x-12)`

Now we will factor the quadratic equation.

`==> y= (x-2)(x+4)(x-3) `

Then, the zeros are:

x= { 2, 3, -4}