The zero-product rule

A product is zero exactly when at least one factor is zero. Thus A(x)B(x)=0 means A(x)=0 or B(x)=0. If both factors were nonzero, their product could not be zero. The rule needs zero on one side; it does not split a product equal to another number. Rearrange to zero, clear any numerical denominators, factorise completely, solve each factor, then check restrictions from the original question. Example 3x2-6x=0 3x(x-2)=0 x=0 or 2 Exam check: dividing by x would lose the valid root x=0. In a length problem, a negative algebraic root may be invalid.