What is factor 27x^3-54x^2+36x-8 ?

The solution to factor 27x^3-54x^2+36x-8 is (3x-2)^3

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factor 27x^3-54x^2+36x-8

factor

27 x^{3} - 54 x^{2} + 36 x - 8

(3 x - 2)^{3}

Solution steps

27 x^{3} - 54 x^{2} + 36 x - 8

Use the rational root theorem

= (3 x - 2) \frac{27 x ^{3} - 54 x ^{2} + 36 x - 8}{3 x - 2}

\frac{27 x ^{3} - 54 x ^{2} + 36 x - 8}{3 x - 2} = 9 x^{2} - 12 x + 4

= (3 x - 2) (9 x^{2} - 12 x + 4)

Factor

9 x^{2} - 12 x + 4 : (3 x - 2) (3 x - 2)

= (3 x - 2) (3 x - 2) (3 x - 2)

Apply exponent rule:

aaa = a^{3}

(3 x - 2) (3 x - 2) (3 x - 2) = (3 x - 2)^{3}

= (3 x - 2)^{3}

(\frac{1}{3} t)^{2}

1 + 1 + 1

\frac{- 3 ^{3}}{3}

27 x^{3} - 216

What is factor 27x^3-54x^2+36x-8 ?
The solution to factor 27x^3-54x^2+36x-8 is (3x-2)^3