What is factor x^4-3x^3-27x+81 ?

The solution to factor x^4-3x^3-27x+81 is (x-3)^2(x^2+3x+9)

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factor x^4-3x^3-27x+81

factor

x^{4} - 3 x^{3} - 27 x + 81

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

Solution steps

x^{4} - 3 x^{3} - 27 x + 81

= (x^{4} - 3 x^{3}) + (- 27 x + 81)

Factor out

x^{3}

from

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

Factor out

- 27

from

- 27 x + 81 : - 27 (x - 3)

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

Factor out common term

x - 3

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

Factor

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

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

Apply exponent rule:

aa = a^{2}

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

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

3^{2} = 9

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

x^{3 - 1}

4 y + 5 = 4 y - 6

- a^{4} b^{2} c + 5 a^{3} b c^{2} + a^{2} b^{3}

7 + 6 x = 2 x + 5

What is factor x^4-3x^3-27x+81 ?
The solution to factor x^4-3x^3-27x+81 is (x-3)^2(x^2+3x+9)