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Simplify [(x³ + 15x² + 75x + 125)/(x² – 25)] × (x – 5)

SSC · 2024 · Quantitative Aptitude
Question:
Simplify [(x³ + 15x² + 75x + 125)/(x² – 25)] × (x – 5)

Options

(1) x² + 25
(2) x² + 5x + 25
(3) x² + 10x + 25
(4) x² – 25
Answer: (3) x² + 10x + 25

Explanation:
Numerator = (x+5)³, denominator = (x+5)(x-5). Simplifying: (x+5)²(x-5)/(x-5) = (x+5)² = x²+10x+25

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