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

2 Answers
Alan P.
Jun 28, 2016

(x+2)(x-2)^2

Explanation:

x^3-2x^2-4x+8

grouping:
color(white)("XXX")=color(red)(""(x^3-2x^2))+color(blue)(""(-4x+8))

color(white)("XXX")=color(red)(x^2(x-2))+color(blue)((-4)(x-2))

color(white)("XXX")=(color(red)(x^2)color(blue)(-4))(x-2)

color(white)("XXX")=color(green)(""(x^2-4))(x-2)

then using difference of squares:
color(white)("XXX")=color(green)((x+2)(x-2))(x-2)

color(white)("XXX")=(x+2)(x-2)^2

Jim G.
Jun 28, 2016

(x-2)^2(x+2)

Explanation:

grouping in 'pairs' gives.

[x^3-2x^2]+[-4x+8]

factorising each pair.

x^2(x-2)-4(x-2)

'Taking out' a common factor of (x - 2)

(x-2)(x^2-4)........ (A)

x^2-4 color(blue)" is a difference of squares" and factorises

color(red)(|bar(ul(color(white)(a/a)color(black)(a^2-b^2=(a-b)(a+b))color(white)(a/a)|)))

x^2=(x)^2" and " 4=(2)^2rArra=x" and "b=2

rArrx^2-4=(x-2)(x+2)

Substituting in (A) : (x-2)(x-2)(x+2)

rArrx^3-2x^2-4x+8=(x-2)^2(x+2)

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