Single remainder condition to find constant

One remainder or factor condition is given to find a single unknown constant, with no further factorisation required.

5 questions · Easy -1.0

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Edexcel P2 2024 January Q1
3 marks Easy -1.2
1. $$f ( x ) = a x ^ { 3 } + 3 x ^ { 2 } - 8 x + 2 \quad \text { where } a \text { is a constant }$$ Given that when \(\mathrm { f } ( x )\) is divided by \(( x - 2 )\) the remainder is 3 , find the value of \(a\).
OCR MEI C1 2008 January Q6
3 marks Moderate -0.8
6 When \(x ^ { 3 } + k x + 7\) is divided by \(( x - 2 )\), the remainder is 3 . Find the value of \(k\).
OCR MEI C1 2007 January Q4
3 marks Moderate -0.8
4 When \(x ^ { 3 } + k x + 5\) is divided by \(x - 2\), the remainder is 3 . Use the remainder theorem to find the value of \(k\).
OCR MEI C1 2010 January Q7
3 marks Easy -1.2
7 When \(x ^ { 3 } + 2 x ^ { 2 } + 5 x + k\) is divided by ( \(x + 3\) ), the remainder is 6 . Find the value of \(k\).
OCR MEI C1 2006 January Q6
3 marks Easy -1.2
When \(x^3 + 3x + k\) is divided by \(x - 1\), the remainder is 6. Find the value of \(k\). [3]