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Algebraic Methods

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Question 150

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+m

where 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):

a.

Show that 16k+m=−816k + m = -816k+m=−8.

[2]
b.

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.

[2]
c.

Hence find the value of k k\,k and the value of mmm.

[4]
d.

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).

[2]
Markscheme

Algebraic Methods Questions

  1. A Level
  2. /Maths
  3. /Algebraic Methods

368 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division. Each one has a worked solution and a mark scheme showing where the marks go.

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