a. Factorise completely x 3 6x 2 + 9x. b. Sketch the curve of y =

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a. Factorise completely x3 − 6x2 + 9x.

b. Sketch the curve of y = x3 − 6x2 + 9x showing clearly the coordinates of the points where the curve touches or crosses the axes.

c. The point with coordinates (−4, 0) lies on the curve with equation y = (x − k)3 − 6(x − k)2 + 9(x − k) where k is a constant. Find the two possible values of k.

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