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.

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

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

How do you factor 8x³+4x²-2x-18x³+4x²-2x-1?