Zero Product Property
Apply the zero product property in Grade 10 algebra. Set each factor equal to zero when a product equals zero and solve for the variable to find all roots of factored equations.
Key Concepts
Property: Let $a$ and $b$ be real numbers. If $ab = 0$, then $a = 0$ or $b = 0$. This rule is the key to solving factored polynomial equations. Once an equation is factored and set equal to zero, you can create mini equations by setting each factor equal to zero to find all possible solutions.
Solve $(x 3)(x + 6) = 0$: $x = 3$ or $x = 6$ Solve $(4x 30)(4x + 30) = 0$: $x = 7.5$ or $x = 7.5$ Solve $2y(y 8) = 0$: $y = 0$ or $y = 8$.
This property is the ultimate detective tool for solving equations. If a group of factors multiply to zero, one of them has to be the culprit! It's the only way the product can be zero. So, after you factor an equation like $(x 2)(x+5)=0$, you just have to interrogate each piece: set $x 2=0$ and $x+5=0$ to find your solutions.
Common Questions
What is the zero product property?
If a × b = 0, then a = 0 or b = 0 (or both). When a product equals zero, at least one factor must be zero. This is the key principle for solving factored polynomial equations.
How do you use the zero product property to solve (x-3)(x+5) = 0?
Set each factor equal to zero: x - 3 = 0 gives x = 3, and x + 5 = 0 gives x = -5. Both values are solutions to the equation.
Why must you factor completely before applying the zero product property?
Each factor must be a complete unit. If you skip factoring steps, you may miss solutions. Factor out GCF first, then factor further until all factors are linear or irreducible.