f(x)=2x3−x2−8x+4f(x) = 2x^3 - x^2 - 8x + 4f(x)=2x3−x2−8x+4
Use the factor theorem to show that (x+2)(x + 2)(x+2) is a factor of f(x)f(x)f(x)
Hence, showing all your working, write f(x)f(x)f(x) as a product of three linear factors.
The finite region R R\,R is bounded by the curve with equation y=f(x)y = f(x)y=f(x) and the xxx-axis, and lies below the xxx-axis. Find, using algebraic integration, the exact value of the area of RRR.