1.5.6 Polynomials and rational expressions

A model for the concentration of a catalyst, $C$ , at a distance $x\,$ millimetres from the center of a reaction chamber is given by the function

C(x) = (x - 4)(3x^2 + 16x + k) + 340

where $k\,$ is a constant.

State the value of the concentration at $x = 4$ .

[1]

Given that $(3 x - 2)$ is a factor of $C (x)$ ,

show that $k = 90$ .

[4]

Hence

(i) fully factorise the expression for $C (x)$ ,

(ii) determine the number of real values of $x\,$ for which the concentration is zero, giving a reason for your answer.

[5]

1.5.6 Polynomials and rational expressions Questions