trig
posted by Bradley on .
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)

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
(3x4)(x+2) close
(3x+4)(x2) aha
so all the roots are
4
4/3
+2