Math 209-College Mathematics II

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How do you factor this completely:
x^3 + ax + 3a + 3x^2

  • Math 209-College Mathematics II -

    You are in luck with this one. Two pairs of terms have x + 3 as a common factor.

    x^3 + ax + 3a + 3x^2
    = x^2(x + 3)+ a(x + 3)
    = (x^2 + a)(x + 3)
    = (x + ia)(x - ia)(x + 3)
    (i is the square root of -1)
    Two of the three roots are complex, for real a.

  • Math 209-College Mathematics II -

    X^3+ax+3a+3x^2
    x^2+3x^2+ax+3a
    x(x+3)+a(x+3)
    (x+a)(x+3)
    x= -a, x= -3

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