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### Factor x^4 + 27x

Factoring x^4 + 27x makes use of two concepts:
First, factor a common divisor out of the given expression. The common divisor or common factor in the above expression is x, and it is factored out as follows:
x(x^3 + 27)
Now you have to apply the sum of two cubes formula, because 27 is a cubic number as 27 = 3 * 3 * 3 =  3^3. So rewrite 27 as 3^3,
x(x^3 + 3^3)
In the above expression, you have a sum of two cubes x^3 and 3^3. Thus it can be factored using the sum of two cubes factoring formula a^3 + b^3 = (a + b)(a^2 - ab + b^2),
x(x + 3)(x^2 - 3x + 3^2)
Now simplify by writing 3^2 = 9,
x(x + 3)(x^2 - 3x + 9)
Thus you have completely factored the expression x^4 + 27x into x(x + 3)(x^2 - 3x + 9)