4. a) Factorise the following: 5. Some chickens are kept in a square enclosure with sides measuring x metres. If the number of chickens is increased, the enclosure will have to be made bigger. The enclosure will have 1 metre added to one side and 2 metres added to the adjacent side. a) (i) Draw a labelled diagram of the original enclosure in the space below. (1 mark) (ii) Add to the diagram to show the new enclosure. Mark the lengths of each side on your diagram. b) Find a simplified expression (i.e. no brackets) for the area of the new enclosure (2 marks) c) If the new enclosure has an area of 42 square metres, what were the dimensions of the original enclosure? 6. The profit per car, $?, made when a particular model is manufactured in ?hours is given by the equation: ?= 4? 2 + 200? 1500 a) Sketch a graph showing the relationship between profit (y-axis) and time of manufacture (x-axis). Show the coordinates of the y-intercept only. b) How long does the manufacturing process need to take in order for the company to make the maximum profit? (2 marks) c) What is the maximum profit that can be made by the car company? (2 marks) d) Indicate the position of the turning point on the sketch graph in part (a) and write down the coordinates of this point in the space below. (1 mark) (2 marks)