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

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Expert Answers

hala718 | 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`

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

`x^3 -2x^2`

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`x^2 -14x + 24`

`x^2 -2x `

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`-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}**