| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Year | 2012 |
| Session | Specimen |
| Marks | 5 |
| Topic | Factor & Remainder Theorem |
| Type | Find constants from coefficient conditions |
| Difficulty | Standard +0.3 This is a straightforward polynomial division problem requiring students to equate coefficients after multiplying out (divisor)(quotient) + remainder = dividend. While it involves handling a quartic polynomial and requires careful algebraic manipulation across multiple terms, it's a standard textbook exercise with a clear method and no novel insight required. Slightly easier than average due to its mechanical nature. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
- Complete correct method reaching a remainder and involving subtraction (allow one slip) [M1]
- Obtain at least $x^2 - 3x + k$ [A1]
- Equate remainders [M1]
- $a = -2,\ c = 5$ [A1]
- $b = -3$ [A1]
**Total: 5 marks**5 When $x ^ { 4 } - 4 x ^ { 3 } + 5 x ^ { 2 } + x + a$ is divided by $x ^ { 2 } - x + 1$, the quotient is $x ^ { 2 } + b x + 1$ and the remainder is $c x - 3$. Find the values of the constants $a , b$ and $c$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2012 Q5 [5]}}