CTET PAPER II 2021 · PYQ · Factorization of Quadratics · hard
If 15x² − 26x + 8 = (Ax + B)(Cx + D), where A and C are positive integers, then what is the value of (2A + B − C − 2D)?
A.0✓ Correct
B.1
C.2
D.3
Explanation
Factor 15x² − 26x + 8: find two numbers multiplying to 15 × 8 = 120 and summing to −26: −20 and −6. So 15x² − 20x − 6x + 8 = 5x(3x − 4) − 2(3x − 4) = (5x − 2)(3x − 4). So A = 5, B = −2, C = 3, D = −4. Then 2A + B − C − 2D = 10 − 2 − 3 − (−8) = 10 − 2 − 3 + 8 = 13. Alternative factoring (3x − 4)(5x − 2): A = 3, B = −4, C = 5, D = −2 gives 6 − 4 − 5 + 4 = 1. Taking A = 5, B = −2, C = 3, D = −4 (since both A and C positive integers, both factorings valid). Most likely intended: option (1) = 1 with A = 3, C = 5.
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