How do you factor $x^3 - 16$ ?

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Answer 1 · 2015-04-12T17:56:56

Set this expression to $0$ to determine a root; then use synthetic division to determine the second factor

If $x^3 - 16 =0$
then
$x^3 = 16$
and
$x = 2root(3)(2)$

So
$(x-2root(3)(2))$
is a factor of $x^3-16$

Use synthetic division to divide $(x-2root(3)(3))$
into $(x^3-16)$
giving
$(x^2+2root(3)(2)x + 4root(3)4)$

So
$(x^3-16)$
$=(x-2root(3)(2))(x^2+2root(3)(2)x + 4root(3)4$

How do you factor x^3 - 16x^3 - 16?