What is factor 1+4x+6x^2+4x^3+x^4 ?

The solution to factor 1+4x+6x^2+4x^3+x^4 is (x+1)^4

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factor 1+4x+6x^2+4x^3+x^4

factor

1 + 4 x + 6 x^{2} + 4 x^{3} + x^{4}

(x + 1)^{4}

Solution steps

1 + 4 x + 6 x^{2} + 4 x^{3} + x^{4}

Write in the standard form

= x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 1

Use the rational root theorem

= (x + 1) \frac{x ^{4} + 4 x ^{3} + 6 x ^{2} + 4 x + 1}{x + 1}

\frac{x ^{4} + 4 x ^{3} + 6 x ^{2} + 4 x + 1}{x + 1} = x^{3} + 3 x^{2} + 3 x + 1

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

Factor

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

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

Simplify

(x + 1) (x + 1)^{3} : (x + 1)^{4}

= (x + 1)^{4}

\frac{4}{5} n + 2 = \frac{2}{5} n - 4

\frac{3 x + 3}{4 x - 1} - \frac{9}{2 x - 3} \leq 0

15 n^{2} + n - 2

\frac{k ^{3}}{k + 5} + \frac{7 k ^{3} + 3}{k + 5}

5 + 9 x - 3 x = 2 + 6 x

What is factor 1+4x+6x^2+4x^3+x^4 ?
The solution to factor 1+4x+6x^2+4x^3+x^4 is (x+1)^4