2 consider the function the function f x 2x ax bx 3 has a factor x 3 w

Question

2. Consider the function, The function f(x) = 2x³ + ax² − bx +3 has a factor (x + 3).
When f(x) is divide by (x - 2), the remainder is 15.
(a) Show that a = 3 and b = 8.
(b) Find the other two factors of f(x).
(c) Find axes intercepts for f(x).
(d) Use calculus to find x-coordinates of turning point for f(x).
Use √57 = 7.55
I
(e) Sketch the graph of y = f(x).
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