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

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

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

factor

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

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

Solution steps

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

Use the rational root theorem

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

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

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

Factor

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

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

Apply exponent rule:

aa = a^{2}

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

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

x^{2} - 11 x = - 30

(x - 1) (x - 1)

12 d^{2} + 4 d - 1

(7 x^{2} y^{3}) (3 x^{5} y^{8})

128 x^{2} + 96 x y + 18 y^{2}

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