What is factor x^5-243 ?

The solution to factor x^5-243 is (x-3)(x^4+3x^3+9x^2+27x+81)

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factor x^5-243

factor

x^{5} - 243

(x - 3) (x^{4} + 3 x^{3} + 9 x^{2} + 27 x + 81)

Solution steps

x^{5} - 243

Rewrite

243

3^{5}

= x^{5} - 3^{5}

Apply factoring rule:

x^{n} - y^{n} = (x - y) (x^{n - 1} + x^{n - 2} y + \dots + x y^{n - 2} y^{n - 1})

x^{5} - 3^{5} = (x - 3) (x^{4} + 3 x^{3} + 3^{2} x^{2} + 3^{3} x + 3^{4})

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

Simplify

(x - 3) (x^{4} + 3 x^{3} + 3^{2} x^{2} + 3^{3} x + 3^{4}) : (x - 3) (x^{4} + 3 x^{3} + 9 x^{2} + 27 x + 81)

= (x - 3) (x^{4} + 3 x^{3} + 9 x^{2} + 27 x + 81)

\frac{- 3 - 5}{0 - 2}

\frac{2 m ^{6}}{3 ( m ^{2} ) ^{3}}

5 \frac{6}{4} - \frac{3}{4}

(3 c - 2 y)^{2}

\frac{x ^{2}}{16} + \frac{x ^{2}}{9}

What is factor x^5-243 ?
The solution to factor x^5-243 is (x-3)(x^4+3x^3+9x^2+27x+81)