Skip to content

Course home

Algebraic Methods

Algebraic Methods

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261
Question 245

The internal stress in a structural component is modeled by the cubic polynomial S(x)=3x3+Ax2+Bx−10S(x) = 3x^3 + Ax^2 + Bx - 10S(x)=3x3+Ax2+Bx−10, where AAA and BBB are integer constants and xxx represents the position along the component.

It is known that:

  • when S(x)S(x)S(x) is divided by (x−2)(x - 2)(x−2), the remainder is RRR
  • when S(x)S(x)S(x) is divided by (x+1)(x + 1)(x+1), the remainder is −2R-2R−2R
  • RRR is a real constant
a.

Show that 3A+B=−53A + B = -53A+B=−5.

[4]
b.

Given that the stress is zero at position x=23x = \frac{2}{3}x=32​, such that (3x−2)(3x - 2)(3x−2) is a factor of S(x)S(x)S(x), find the value of AAA and the value of BBB.

[3]
c.

Hence determine the quadratic expression Q(x)Q(x)Q(x) such that S(x)=(3x−2)Q(x)S(x) = (3x - 2)Q(x)S(x)=(3x−2)Q(x).

[3]
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.

Question bank