Question

Let f(x) = 14x^3 + 28x^2 – 46x and g(x) = 2x + 7. which is the solution set to the equation 1/12 f(x) = g(x)? *

Answer 1

A graphing calculator shows the solution set of
(1/12)f(x) - g(x) = 0
to be x ∈ {-3, -1, 2}

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The equation (1/12)f(x) = g(x) can be rewritten to be f(x) = 12g(x).
14x^3 +28x^2 -46x = 24x + 84
14x^3 +28x^2 -70x -84 = 0 . . . . subtract the right side
x^3 +2x^2 -5x -6 = 0 . . . . . . . . . put in standard form
The rational root theorem tells you integer roots will be among ±1, ±2, ±3. Checking -1 tells you that is a root, so the equation factors like this:
(x +1)(x^2 +x -6) = (x+1)(x+3)(x-2) = 0