Question

Solve using polynomial equations by factoring and using the principle of zero product.

Answer 1

Here x^3-27=0 can be written as
x^3=27 and it also can be,
x^3=3^3
then on comparing both we got ,
x=3..
Hope it will satisfy you

Answer 2

(x-3)(x^2+3x+27) = 0
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Solve the quadratic factor:
x^2 + 3x + 27 = 0

x = [-3 +- sqrt(9-4*27)/2
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x = [-3 +- sqrt(-99)]/2
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x = [-3+-3sqrt(11)i]/2 (2 complex number solutions)
x = 3 (the Real Number solution)