# How do you factor #4y=x^3-4x^2-11x+30 #?

##### 1 Answer

Sep 2, 2016

#### Explanation:

By the rational roots theorem, any *rational* zeros of

That means that the only possible *rational* zeros are:

#+-1, +-2, +-3, +-5, +-6, +-10, +-15, +-30#

If

#x^3-4x^2-11x+30 = (8)-4(4)-11(2)+30 = 8-16-22+30 = 0#

So

#x^3-4x^2-11x+30 = (x-2)(x^2-2x-15)#

To factor the remaining quadratic, find a pair of numbers with difference

#x^2-2x-15 = (x-5)(x+3)#

Putting it all together, we have:

#4y = (x-2)(x-5)(x+3)#