How do you factor #8x³+4x²-2x-1#?

1 Answer
Dec 13, 2015

Answer:

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

Explanation:

"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)#