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trig

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The equation f(x) = 3x^3 + 10x^2 - 16x - 32 has a root at x = -4

a) Find the depressed equation using synthetic division and the root given. Factor out any constants that may appear.

b) Factor the depressed equation (which is now a quadratic) using any method EXCEPT synthetic division.

c) List all the roots for f(x)

  • trig -

    They told you that x = -4 was a root so (x+4) is a factor so divide 3x^3 + 10x^2 - 16x - 32 by (x+4)

    I get
    3 x^2 - 2 x - 8

    Factor that
    3 * 1 factors 3
    8*1 or 2*4 factors 8
    so try 2 and 4
    (3x -2)(x+4), nope
    (3x-4)(x+2) close
    (3x+4)(x-2) aha
    so all the roots are
    -4
    -4/3
    +2

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