The power output P P\,P in kilowatts of a specialized wind turbine is modeled by the function P(x)=2x3+kx2−25x+cP(x) = 2x^3 + kx^2 - 25x + cP(x)=2x3+kx2−25x+c, where x x\,x is the wind speed in ms−1\text{ms}^{-1}ms−1 and k,c k, c\,k,c are constants.
At a wind speed of 0.5 ms-1, the turbine produces no power. Show that k+4c=49k + 4c = 49k+4c=49.
It is determined that at a wind speed of 2 ms-1, the power output is exactly c−30c - 30c−30. Determine the value of k k\,k and the value of ccc.
Using algebraic division or otherwise, fully factorise the expression for P(x)P(x)P(x).
302 exam-style questions on WJEC A Level Maths 1.2 Algebra and Functions, covering 1.2.1 Algebra and Functions, 1.2.2 Algebra and Functions, 1.2.3 Algebra and Functions, 1.2.4 Algebra and Functions, 1.2.5 Algebra and Functions, 1.2.6 Algebra and Functions, 1.2.7 Algebra and Functions, 1.2.8 Algebra and Functions, 1.2.9 Algebra and Functions, 1.2.10 Algebra and Functions, 1.2.11 Algebra and Functions, and 1.2.12 Algebra and Functions. Each one has a worked solution and a mark scheme showing where the marks go.