A model for the concentration of a catalyst, CCC, at a distance x x\,x millimetres from the center of a reaction chamber is given by the function
C(x)=(x−4)(3x2+16x+k)+340 C(x) = (x - 4)(3x^2 + 16x + k) + 340 C(x)=(x−4)(3x2+16x+k)+340where k k\,k is a constant.
State the value of the concentration at x=4x = 4x=4.
Given that (3x−2)(3x - 2)(3x−2) is a factor of C(x)C(x)C(x),
show that k=90k = 90k=90.
Hence
(i) fully factorise the expression for C(x)C(x)C(x),
(ii) determine the number of real values of x x\,x for which the concentration is zero, giving a reason for your answer.
