What is factor 1+243x^5 ?

The solution to factor 1+243x^5 is (3x+1)(81x^4-27x^3+9x^2-3x+1)

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factor 1+243x^5

factor

1 + 243 x^{5}

(3 x + 1) (81 x^{4} - 27 x^{3} + 9 x^{2} - 3 x + 1)

Solution steps

1 + 243 x^{5}

Write in the standard form

= 243 x^{5} + 1

Apply exponent rules

= (3 x)^{5} + 1^{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}), n i s o dd

(3 x)^{5} + 1^{5} = (3 x + 1) (3^{4} x^{4} - 3^{3} x^{3} + 3^{2} x^{2} - 3 x + 1)

= (3 x + 1) (3^{4} x^{4} - 3^{3} x^{3} + 3^{2} x^{2} - 3 x + 1)

Simplify

(3 x + 1) (3^{4} x^{4} - 3^{3} x^{3} + 3^{2} x^{2} - 3 x + 1) : (3 x + 1) (81 x^{4} - 27 x^{3} + 9 x^{2} - 3 x + 1)

= (3 x + 1) (81 x^{4} - 27 x^{3} + 9 x^{2} - 3 x + 1)

(9^{2})^{3}

\frac{cos ( x )}{1 - sin ( x )} - \frac{cos ( x )}{1 + sin ( x )}

(2 x + 5) (3 x - 1)

\frac{27}{90}

\frac{2}{5} \cdot \frac{3}{2}

What is factor 1+243x^5 ?
The solution to factor 1+243x^5 is (3x+1)(81x^4-27x^3+9x^2-3x+1)