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Mathematics · Oct / Nov 2025 · Paper 21 · Question 22

0580

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0580/21/O/N/25 © UCLES 2025 22 Solve. x x x 1 2 2 Ä ¢ Ë x ¢ or x ¢ [5]

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–1 and 4 [5]

B2 for x2 – 3x – 4 [= 0]

or M1 for 2(x + 2) = x(x – 1) or better

M2 for a correct method to solve their three-term quadratic in the numerator

or M1 for (x + a)(x + b) where ab = –4 or a + b = –3 or ( − + − x x 4) [1]( x 4) or + − + x x ( 1) 4( x 1) − 2 −× ×− or better

or M1 for ( 3) 4 [1]

4 + − p q p q or if in the form or then r r

M1 for p = −(−3) and r = 2(1) or better

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