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

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

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factor x^4+2x^3+2x^2+2x+1

factor

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

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

Solution steps

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

Use the rational root theorem

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

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

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

Factor

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

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

Apply exponent rule:

aa = a^{2}

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

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

\frac{8}{9} \div \frac{4}{9}

\frac{18}{60}

\frac{1}{x} - \frac{1}{x + 2}

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

\frac{7}{49}

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