Concept:The expression (x−a)(x−b)(x−c) expands to a cubic polynomial in x with coefficients expressed in terms of the sum and sum of products of a,b,c.Explanation:First, multiply the first two factors:(x−a)(x−b)=x2−(a+b)x+abNow multiply this result by (x−c):[x2−(a+b)x+ab](x−c)=x2(x−c)−(a+b)x(x−c)+ab(x−c)=x3−cx2−(a+b)x2+(a+b)cx+abx−abcCombine like terms:x3−[c+(a+b)]x2+[(a+b)c+ab]x−abcx3−(a+b+c)x2+(ac+bc+ab)x−abcThus the expanded form is x3−(a+b+c)x2+(bc+ca+ab)x−abc.Answer:Option A: x3−(a+b+c)x2+(bc+ca+ab)x−abc