# How do you factor #y= x^3-5x^2-2x+24# ?

##### 1 Answer

Use the rational root theorem to get started, then factor the remaining quadratic to find:

#x^3-5x^2-2x+24 = (x+2)(x-4)(x-3)#

#### Explanation:

Let

By the rational root theorem, any rational zeros of

That means that the only possible rational zeros are the factors of

#+-1, +-2, +-3, +-4, +-6, +-12, +-24#

Try each in turn:

#f(1) = 1-5-2+24 = 18#

#f(-1) = -1-5+2+24 = 20#

#f(2) = 8-20-4+24 = 8#

#f(-2) = -8-20+4+24 = 0#

So

#x^3-5x^2-2x+24 = (x+2)(x^2-7x+12)#

We can factor

#x^2-7x+12 = (x-4)(x-3)#

Putting it all together:

#x^3-5x^2-2x+24 = (x+2)(x-4)(x-3)#