x2-x-6 is a factor of f(x)=3x3+px2+qx+6. Find the values of the constants p and q and state the zeros of f(x).

Answer 1

f(x) = 3x^3 + px^2 + qx + 6

If x^2-x-6 is a factor, so are (x-3) and (x+2)
that is f(3) = 0 and f(-2) = 0
f(3) = 81 + 9p + 3q + 6 = 0 ----> 3p + q = -29
f(-2) = -24 + 4p - 2q + 6 = 0 -----> 2p - q = 9

add them : 5p = -20
etc, take over ....

Answer 2

Is correct, am very happy