Finding Polynomial from Division Information

Questions where the quotient and remainder of a division are given, and you must reconstruct the original polynomial using the division algorithm.

2 questions · Moderate -0.2

1.02j Manipulate polynomials: expanding, factorising, division, factor theorem

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OCR C4 2008 January Q3

5 marks Standard +0.3

3 When \(x ^ { 4 } - 2 x ^ { 3 } - 7 x ^ { 2 } + 7 x + a\) is divided by \(x ^ { 2 } + 2 x - 1\), the quotient is \(x ^ { 2 } + b x + 2\) and the remainder is \(c x + 7\). Find the values of the constants \(a , b\) and \(c\).

OCR C4 2012 January Q1

3 marks Moderate -0.8

1 When the polynomial \(\mathrm { f } ( x )\) is divided by \(x ^ { 2 } + 1\), the quotient is \(x ^ { 2 } + 4 x + 2\) and the remainder is \(x - 1\). Find \(\mathrm { f } ( x )\), simplifying your answer.