How do you factor #24x^3-6x^2+8x-2#?

1 Answer
George C.
Nov 15, 2016

#24x^3-6x^2+8x-2 = 2(3x^2+1)(4x-1)#

Explanation:

Notice that the ratio betweeen the first and second terms is the same as that between the third and fourth terms. So this cubic will factor by grouping:

#24x^3-6x^2+8x-2 = (24x^3-6x^2)+(8x-2)#

#color(white)(24x^3-6x^2+8x-2) = 6x^2(4x-1)+2(4x-1)#

#color(white)(24x^3-6x^2+8x-2) = (6x^2+2)(4x-1)#

#color(white)(24x^3-6x^2+8x-2) = 2(3x^2+1)(4x-1)#

The remaining quadratic factor has no linear factors with Real coefficients, since #3x^2+1 >= 1# for all Real values of #x#.

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