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Factor x 3 – 6 x 2 + 5 x + 12?   Ans:- ⇒ ( x + 1 ) ( x − 3 ) ( x − 4 ) Factors are  x = − 1 , 3 , 4 Explanation: ( x 3 − 6 x 2 + 5 x + 12 ) Since the sum of the coefficients of the terms is zero,  x + 1  is a factor. Using synthetic division, a a a − 1 a a a ∣ a a a 1 a a a − 6 a a a 5 a a a 12 a a a a a a a a a ∣ a a a ⏐ ↓ a a − 1 a a a 7 a − 12 a a a a a a a a a ∣ … … … … … … … … … a a a a a a a a a a a a a a 1 a a a − 7 a a a 12 a a a 0 ⇒ ( x + 1 ) ( x 2 − 7 x + 12 ) ⇒ ( x + 1 ) ( x 2 − 3 x − 4 x + 12 ) ⇒ ( x + 1 ) ( x ( x − 3 ) − 4 ( x − 3 ) ) ⇒ ( x + 1 ) ( x − 3 ) ( x − 4 ) Factors are  x = − 1 , 3 , 4