SLC Mathematics Department 2. g(x) = 2x'+ x2 - 41x-70 (a) Use the factor theorem to show that g(x) is divisible by (x - 5). (2) (b) Hence, showing all your working, write g(x) as a product of three linear factors. (4) The finite region R is bounded by the curve with equation y = g(x) and the x-axis, and lies below the x-axis. (c) Find, using algebraic integration, the exact value of the area of R. (4)