How do you factor: $y= x^3 - 4x^2 + 4x - 16$ ?

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Answer 1 · 2016-03-12T23:13:00

Factor by grouping to find:

$y = x^3-4x^2+4x-16$

$=(x^2+4)(x-4)$

$=(x-2i)(x+2i)(x-4)$

Factor by grouping:

$y = x^3-4x^2+4x-16$

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

$=x^2(x-4)+4(x-4)$

$=(x^2+4)(x-4)$

That's as far as you can go with Real coefficients: $(x^2+4)$ has no linear factors with Real coefficients since $x^2+4 >= 4 > 0$ for all $x in RR$ .

If you allow Complex coefficients then we can go a little further:

$=(x^2-(2i)^2)(x-4)$

$=(x-2i)(x+2i)(x-4)$

How do you factor: y= x^3 - 4x^2 + 4x - 16 y= x^3 - 4x^2 + 4x - 16 ?