Moderate -0.3 This is a straightforward algebraic fraction simplification requiring factorization of both numerator and denominator, then canceling common factors. The numerator factors as a quadratic in x² (difference of squares twice), and the denominator quadratics are already given. While it requires careful algebraic manipulation across multiple steps, it's a standard C4 technique with no novel problem-solving required, making it slightly easier than average.
# Question 1:
| Answer/Working | Marks | Guidance |
|---|---|---|
| Attempt to factorise **both** numerator & denominator | M1 | completely or partially |
| Num = e.g. $(x^2-1)(x^2-9)$ or $(x^2-2x-3)(x^2+2x-3)$ | B1 | or $(x-3)(x+3)(x-1)(x+1)$ |
| Denominator = e.g. $(x^2-2x-3)(x+5)(x+3)$ | B1 | or $(x-3)(x+1)(x+5)(x+3)$ |
| $\frac{x-1}{x+5}$ or $1-\frac{6}{x+5}$ WWW | A1 **4** | ISW but not if any further 'cancellation' |
| **Alternative: long division** | | |
| Expand denom as quartic & attempt to divide $\frac{\text{numerator}}{\text{denominator}}$ | M1 | but not divide $\frac{\text{denominator}}{\text{numerator}}$ |
| Obtain quotient = 1 & remainder = $-6x^3-6x^2+54x+54$ | B1 | |
| Final B1 A1 available as before | | |
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