How do you factor the expression $4x^3 + 6x^2 + 6x + 9$ ?

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Answer 1 · 2015-12-24T00:36:34

Factor by grouping to find:

$4x^3+6x^2+6x+9=(2x^2+3)(2x+3)$

Factor by grouping:

$4x^3+6x^2+6x+9$

$=(4x^3+6x^2)+(6x+9)$

$=2x^2(2x+3)+3(2x+3)$

$=(2x^2+3)(2x+3)$

The remaining quadratic factor $(2x^2+3)$ has no simpler linear factors with Real coefficients since it is non-zero for any Real number $x$ :

$2x^2+3 >= 3 > 0$

If we resort to Complex numbers then it factorises further:

$(2x^2+3) = (sqrt(2)x-sqrt(3)i)(sqrt(2)x+sqrt(3)i)$

How do you factor the expression 4x^3 + 6x^2 + 6x + 94x^3 + 6x^2 + 6x + 9?