How do you factor by grouping: #x^3 - 2x^2 - 4x + 8#?

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Answer 1 · 2015-04-21T09:00:29

To factor this expression, we can make groups of two like this:

#(x^3 - 2x^2) - (4x - 8)#

# = x^2(x-2) - 4(x - 2)#

The factor #x - 2# is common to both the terms

# = (x - 2)(x^2 - 4)#

# = (x - 2)(x^2 - 2^2)#

We also know that #color(blue)(a^2 - b^2 = (a+b)(a-b)#

# = (x - 2)(x + 2)(x - 2)#

#color(green)( = (x - 2)^2*(x+2)# is the factorised form of #x^3 - 2x^2 - 4x + 8#