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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