How do you factor completely #x^3-2x^2-9x+18#?

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Answer 1 · 2017-05-08T02:14:38

#(x-3)(x+3)(x-2)#

Factor by grouping:

#(color(blue)(x^3-2x^2))# #+# #(color(red)(-9x+18))#

Starting on the left we can factor out an #x^2#

#color(blue)(x^2(x-2))#

On the right we can then factor out a #-9#

#color(red)(-9(x-2))#

Observe:

#color(blue)(x^2(x-2))# #+# #color(red)(-9(x-2))#

*Notice how we have two #x-2#. We can then simply rewrite the expression as follows.

#(x^2-9)(x-2)#

*Note: all we did was combine #color(blue)(x^2)# and #color(red)(-9)# and wrote #(x-2)# as one term instead of two.

We're not done just yet. We can still factor #(x^2-9)# into #(x-3)(x+3)#

So a completely factored expression is then:

#(x-3)(x+3)(x-2)#