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                                    Find the H.C.F. of p(x) = 2x3 – 3x2 – 2x + 3 and q(x) = 3x2 + 8x + 5.1. (x + 1)2. (x – 1)3. (2x – 3)4. (2x + 1) | 
                            
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Answer» Correct Answer - Option 1 : (x + 1) Given: p(x) = 2x3 – 3x2 – 2x + 3 and q(x) = 3x2 + 8x + 5 Concept: H.C.F. of two or more equations is the greatest factor that divides each of them exactly. Calculation: The factors of p(x) = 2x3 – 3x2 – 2x + 3 ⇒ x2 × (2x – 3) – 1 × (2x – 3) ⇒ (x2 – 1) × (2x – 3) ⇒ (x – 1) × (x + 1) × (2x – 3) And, the factors of q(x) = 3x2 + 8x + 5 ⇒ 3x2 + 5x + 3x + 5 ⇒ x × (3x + 5) + 1 × (3x + 5) ⇒ (3x + 5) × (x + 1) ∴ The required H.C.F. is (x + 1). | 
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