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.
306 exam-style questions on CCEA A Level Maths 1.1 Algebra and functions, covering 1.1.1 Algebra and functions, 1.1.2 Algebra and functions, 1.1.3 Algebra and functions, 1.1.4 Algebra and functions, 1.1.5 Algebra and functions, 1.1.6 Algebra and functions, 1.1.7 Algebra and functions, 1.1.8 Algebra and functions, 1.1.9 Algebra and functions, 1.1.10 Algebra and functions, 1.1.11 Algebra and functions, 1.1.12 Algebra and functions, 1.1.13 Algebra and functions, and 1.1.14 Algebra and functions. Each one has a worked solution and a mark scheme showing where the marks go.