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(a) The function f ( x ) = x 3 − 4 x 2 − x...

  1. (a) The function f ( x ) = x 3 − 4 x 2 − x + 4 has a factor of x - 4. Using long division, find the remaining factors of f(x).
  1. The function f ( x ) = ax 3 + bx is divided by (x + 3) exactly and has a remainder of -10 when divided by (x − 2) . Find the values of a, b.
  1. (i) Sketch the curve of f ( x ) = x 3 − 9x , showing the values of all intercepts

on both axes.

  1. State the values of x for which f ( x)   0.
  1. Shade and calculate the area bounded by the curve and the x-axis.
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