| Exam Board | Edexcel |
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| Module | C12 (Core Mathematics 1 & 2) |
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| Year | 2015 |
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| Session | June |
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| Topic | Factor & Remainder Theorem |
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| Type | Two unknowns, direct system |
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2.
$$f ( x ) = x ^ { 4 } - x ^ { 3 } + 3 x ^ { 2 } + a x + b$$
where \(a\) and \(b\) are constants.
When \(\mathrm { f } ( x )\) is divided by \(( x - 1 )\) the remainder is 4
When \(\mathrm { f } ( x )\) is divided by \(( x + 2 )\) the remainder is 22
Find the value of \(a\) and the value of \(b\).