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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)

  • algebra -

    You get the "depressed equation" by dividing
    3x^3 + 10x^2 - 16x - 32 by the factor already. This is a skil you need to learn.
    x + 4. Read up on how to do synthetic division if you don't know already. Show your work if you need additional help.

    The depressed quadratic equation (if f(x) - 0) is
    3x^2 -2x -8 = 0

    That does not factor easily

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