1.5 Algebraic Division
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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]

1.5 Algebraic Division Questions

Practise Edexcel A Level Maths 1.5 Algebraic Division with exam-style questions for A Level Maths. 65 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

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1.5 Algebraic Division Questions

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