AP DSC School Assistant Math Model Test 1

Concept:HCF (Highest Common Factor) is the common polynomial factor shared by both expressions, and LCM (Least Common Multiple) is the product of all distinct polynomial factors, each taken with the highest exponent that appears in any expression.Explanation:Factor the first polynomial: $x^{2}-11x+24 = x^{2}-3x-8x+24 = x(x-3)-8(x-3) = (x-3)(x-8)$.Factor the second polynomial: $x^{2}-13x+40 = x^{2}-8x-5x+40 = x(x-8)-5(x-8) = (x-8)(x-5)$.The common factor is $(x-8)$ — this is the HCF.The LCM is the product of all distinct factors: $(x-5)(x-8)(x-3)$.Answer:Option C: $(x - 8)$, $(x - 5)(x - 8)(x - 3)$