What is factor p^{21}+1 ?

The solution to factor p^{21}+1 is (p+1)(p^6-p^5+p^4-p^3+p^2-p+1)(p^{14}-p^7+1)

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factor p^{21}+1

factor

p^{21} + 1

(p + 1) (p^{6} - p^{5} + p^{4} - p^{3} + p^{2} - p + 1) (p^{14} - p^{7} + 1)

Solution steps

p^{21} + 1

Apply exponent rules

= (p^{7})^{3} + 1^{3}

Apply Sum of Cubes Formula:

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

(p^{7})^{3} + 1^{3} = (p^{7} + 1) (p^{14} - p^{7} + 1)

= (p^{7} + 1) (p^{14} - p^{7} + 1)

Factor

p^{7} + 1 : (p + 1) (p^{6} - p^{5} + p^{4} - p^{3} + p^{2} - p + 1)

= (p + 1) (p^{6} - p^{5} + p^{4} - p^{3} + p^{2} - p + 1) (p^{14} - p^{7} + 1)

\frac{\frac{7}{3}}{x} - 1 + \frac{\frac{7}{6}}{x} + 2 - \frac{\frac{1}{2}}{x}

x^{4} + 2 x^{2} \cdot y^{2} + y^{4}

3 a^{7} \cdot b - 24 a^{4} \cdot b^{4}

(3 q + 1)^{3}

(2 z - 3 w)^{3}

What is factor p^{21}+1 ?
The solution to factor p^{21}+1 is (p+1)(p^6-p^5+p^4-p^3+p^2-p+1)(p^{14}-p^7+1)