What is factor 4x^4+4x^3+5x^2+4x+1 ?

The solution to factor 4x^4+4x^3+5x^2+4x+1 is (2x+1)^2(x^2+1)

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factor 4x^4+4x^3+5x^2+4x+1

factor

4 x^{4} + 4 x^{3} + 5 x^{2} + 4 x + 1

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

Solution steps

4 x^{4} + 4 x^{3} + 5 x^{2} + 4 x + 1

Use the rational root theorem

= (2 x + 1) \frac{4 x ^{4} + 4 x ^{3} + 5 x ^{2} + 4 x + 1}{2 x + 1}

\frac{4 x ^{4} + 4 x ^{3} + 5 x ^{2} + 4 x + 1}{2 x + 1} = 2 x^{3} + x^{2} + 2 x + 1

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

Factor

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

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

Apply exponent rule:

aa = a^{2}

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

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

t^{2} + 6 t + 8

1 - ln (x) \geq 0

\frac{1}{7} \cdot \frac{7}{11}

\frac{1}{3} (3)

6 x + 5 < - 1 or 1 - 2 x < 7

What is factor 4x^4+4x^3+5x^2+4x+1 ?
The solution to factor 4x^4+4x^3+5x^2+4x+1 is (2x+1)^2(x^2+1)