What is factor x^4-2x^3+27x-54 ?

The solution to factor x^4-2x^3+27x-54 is (x-2)(x+3)(x^2-3x+9)

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factor x^4-2x^3+27x-54

factor

x^{4} - 2 x^{3} + 27 x - 54

(x - 2) (x + 3) (x^{2} - 3 x + 9)

Solution steps

x^{4} - 2 x^{3} + 27 x - 54

= (x^{4} - 2 x^{3}) + (27 x - 54)

Factor out

x^{3}

from

x^{4} - 2 x^{3} : x^{3} (x - 2)

Factor out

27

from

27 x - 54 : 27 (x - 2)

= x^{3} (x - 2) + 27 (x - 2)

Factor out common term

x - 2

= (x - 2) (x^{3} + 27)

Factor

x^{3} + 27 : (x + 3) (x^{2} - 3 x + 3^{2})

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

3^{2} = 9

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

x (2 x + 4) = 0

2 x + 12 \leq 2 x + 12

8 - 2 x \leq 2

\frac{x ^{2} - 16}{x ^{2} - 36} \leq 0

\frac{9}{3} + 4

What is factor x^4-2x^3+27x-54 ?
The solution to factor x^4-2x^3+27x-54 is (x-2)(x+3)(x^2-3x+9)