What is factor x^{n+3}+x^n+x^4+x ?

The solution to factor x^{n+3}+x^n+x^4+x is (x^2+1-x)(1+x)(x^n+x)

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factor x^{n+3}+x^n+x^4+x

factor

x^{n + 3} + x^{n} + x^{4} + x

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

Solution steps

x^{n + 3} + x^{n} + x^{4} + x

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

= x^{3} x^{n} + x^{n} + x^{4} + x

Factor out common term

x^{n}

= x^{n} (x^{3} + 1) + x^{4} + x

Factor

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

= x^{4} + x + x^{n} (x + 1) (x^{2} - x + 1)

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

x^{4} = x x^{3}

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

Factor out common term

x

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

Factor

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

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

Factor out common term

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

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

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ln (e^{3 c - 2 x} + e^{- x})

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