Algebraic identity, find constants

A question is this type if and only if it presents a polynomial identity (e.g. 5x^2 + px - 8 ≡ q(x-1)^2 + r) and asks for the values of the unknown constants by expanding and comparing coefficients.

4 questions · Moderate -0.8

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OCR C1 Q1
3 marks Moderate -0.8
  1. \(\quad \mathrm { f } ( x ) = ( \sqrt { x } + 3 ) ^ { 2 } + ( 1 - 3 \sqrt { x } ) ^ { 2 }\).
Show that \(\mathrm { f } ( x )\) can be written in the form \(a x + b\) where \(a\) and \(b\) are integers to be found.
OCR C1 2012 January Q3
4 marks Moderate -0.8
3 Given that $$5 x ^ { 2 } + p x - 8 = q ( x - 1 ) ^ { 2 } + r$$ for all values of \(x\), find the values of the constants \(p , q\) and \(r\).
OCR MEI FP1 2009 January Q2
4 marks Moderate -0.8
2 Find the values of \(A , B\) and \(C\) in the identity \(2 x ^ { 2 } - 13 x + 25 \equiv A ( x - 3 ) ^ { 2 } - B ( x - 2 ) + C\).
OCR MEI FP1 2010 June Q1
4 marks Moderate -0.8
1 Find the values of \(A , B\) and \(C\) in the identity \(4 x ^ { 2 } - 16 x + C \equiv A ( x + B ) ^ { 2 } + 2\).