Factor the polynomial completely x^3+27
Use the identity:
x³+y³
=(x+y)(x²-xy+y²)
where
x=x, y=3
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To factor the polynomial x^3 + 27 completely, we can use the sum of cubes formula. The sum of cubes formula states that a^3 + b^3 can be factored as (a + b)(a^2 - ab + b^2).
In this case, the expression x^3 + 27 can be seen as (x^3 + 3^3), where a = x and b = 3. Now we can use the sum of cubes formula to factor it as:
(x + 3)(x^2 - 3x + 9)
So the factored form of x^3 + 27 is (x + 3)(x^2 - 3x + 9).