How do you factor #8x³+4x²-2x-1#?

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Answer 1 · 2015-12-13T16:39:35

#(2x+1)^2(2x-1)#

"Group" the polynomial into two parts:

#color(blue)(8x^3+4x^2)color(red)(-2x-1)#

Factor out a common term from either section.

#color(blue)(4x^2(2x+1))color(red)(-1(2x+1))#

Notice that a #2x+1# term can be factored out.

#(2x+1)color(purple)((4x^2-1)#

Notice that #4x^2-1# is a difference of squares.

#(2x+1)color(purple)((2x+1)(2x-1))#

#(2x+1)^2(2x-1)#