A structural engineer models the stress L(x)L(x)L(x) on a cantilever beam at a distance x x\,x from the support as
L(x)=x3+(k−3)x2−2x+m L(x) = x^3 + (k - 3)x^2 - 2x + m L(x)=x3+(k−3)x2−2x+mwhere k k\,k and m m\,m are constants and k>0k > 0k>0.
Given that (x−4)(x - 4)(x−4) is a factor of L(x)L(x)L(x):
Show that 16k+m=−816k + m = -816k+m=−8.
Given also that when L(x)L(x)L(x) is divided by (x+k)(x + k)(x+k), the remainder is -48:
Show that 3k2−2k−m−48=03k^2 - 2k - m - 48 = 03k2−2k−m−48=0.
Hence find the value of k k\,k and the value of mmm.
Find a quadratic expression g(x)g(x)g(x) such that L(x)=(x−4)g(x)L(x) = (x - 4)g(x)L(x)=(x−4)g(x).
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.