Factorizex3−6x2+11x−6=0Letf(x)=x3−6x2+11x−6=0Substitutex=0,±1,±2,⋯f(0)=−6,f(1)=13−6(12)+11(1)−6=1−6+11−6=0Sincef(1)=0,By Factor theoremx−1is a factor of the polynomialDivide the polynomialby the factorx2−5x+6x−1∣x3−6x2+11x−6=0−(x3−x2)=−5x2+11x−6−(−5x2+5x)=6x−6−(6x−6)=0Factorize the quotientx2−5x+6=(x−3)(x−2)f(x)=divisor×quotientTherefore,x3−6x2+11x−6=(x−1)(x−2)(x−3)
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