What is factor x^{10}+x^8+x^6+x^4+x^2+1 ?

The solution to factor x^{10}+x^8+x^6+x^4+x^2+1 is (x^2+x+1)(x^2-x+1)(x^2+1)(x^4-x^2+1)

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factor x^{10}+x^8+x^6+x^4+x^2+1

factor

x^{10} + x^{8} + x^{6} + x^{4} + x^{2} + 1

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

Solution steps

x^{10} + x^{8} + x^{6} + x^{4} + x^{2} + 1

Let

u = x^{2}

= u^{5} + u^{4} + u^{3} + u^{2} + u + 1

Factor

u^{5} + u^{4} + u^{3} + u^{2} + u + 1 : (u^{2} + u + 1) (u + 1) (u^{2} - u + 1)

= (u^{2} + u + 1) (u + 1) (u^{2} - u + 1)

Substitute back

u = x^{2}

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

Factor

x^{4} + x^{2} + 1 : (x^{2} + 1 + x) (x^{2} + 1 - x)

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

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

\frac{2}{x + 3} - \frac{1}{x ^{2} + 7 x + 12}

\frac{3}{4} \div \frac{5}{7}

(sec^{2} (x) + csc^{2} (x)) - (tan^{2} (x) + cot^{2} (x))

\frac{8 6 mn + 6 8 mn}{2 2 mn}

What is factor x^{10}+x^8+x^6+x^4+x^2+1 ?
The solution to factor x^{10}+x^8+x^6+x^4+x^2+1 is (x^2+x+1)(x^2-x+1)(x^2+1)(x^4-x^2+1)