What is factor n^4+2n^3+2n^2+2n+1 ?

The solution to factor n^4+2n^3+2n^2+2n+1 is (n+1)^2(n^2+1)

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factor n^4+2n^3+2n^2+2n+1

factor

n^{4} + 2 n^{3} + 2 n^{2} + 2 n + 1

(n + 1)^{2} (n^{2} + 1)

Solution steps

n^{4} + 2 n^{3} + 2 n^{2} + 2 n + 1

Use the rational root theorem

= (n + 1) \frac{n ^{4} + 2 n ^{3} + 2 n ^{2} + 2 n + 1}{n + 1}

\frac{n ^{4} + 2 n ^{3} + 2 n ^{2} + 2 n + 1}{n + 1} = n^{3} + n^{2} + n + 1

= (n + 1) (n^{3} + n^{2} + n + 1)

Factor

n^{3} + n^{2} + n + 1 : (n + 1) (n^{2} + 1)

= (n + 1) (n + 1) (n^{2} + 1)

Apply exponent rule:

aa = a^{2}

(n + 1) (n + 1) = (n + 1)^{2}

= (n + 1)^{2} (n^{2} + 1)

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\frac{( 3 x - 5 )}{4} - \frac{( x + 7 )}{8}

\frac{8 l ^{'} 1}{4 l}

What is factor n^4+2n^3+2n^2+2n+1 ?
The solution to factor n^4+2n^3+2n^2+2n+1 is (n+1)^2(n^2+1)