Why does the zero product property work? Algebra Polynomials and Factoring Zero Product Principle 1 Answer Wataru Oct 26, 2014 If #a cdot b=0#, then at least one of #a# and #b# must be zero since if #a# and #b# were nonzero, then #a cdot b# would be nonzero; therefore, #a cdot b=0# means that #a=0#, #b=0#, or both. I hope that this was helpful. Answer link Related questions What is the Zero Product Principle? How to use the zero product principle to find the value of x? How do you solve the polynomial #10x^3-5x^2=0#? Can you apply the zero product property in the problem #(x+6)+(3x-1)=0#? How do you solve the polynomial #24x^2-4x=0#? How do you use the zero product property to solve #(x-5)(2x+7)(3x-4)=0#? How do you factor and solve #b^2-\frac{5}{3b}=0#? How do you solve #(x - 12)(5x - 13) = 0#? How do you solve #(2u+7)(3u-1)=0#? How do you solve #(2m + 3)(4m + 3) = 0#? See all questions in Zero Product Principle Impact of this question 3846 views around the world You can reuse this answer Creative Commons License