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What's the Zero Product Property?

Definition: Zero Product Property

Summary

  1. a, b, and c are variables that represent factors being multiplied
  2. A factor is just something that is being multiplied
  3. Factors can be numbers, variables, or expressions
  4. Multiplying by 0 makes the whole expression equal 0
  5. So if we multiply several factors and the result is 0, then we know one of the factors must equal 0
  6. x and x+2 are factors being multiplied
  7. Since multiplying x and x+2 gives a result of 0, either x=0 or x+2=0

Notes

    1. If you multiply anything by 0, it makes everything equal 0
    2. Factors are just the things being multiplied together
    3. So this property tells us that if we multiply several things and get 0, one of the things we were multiplying has to be 0
    1. a, b, and c are variables that can be any factor
    1. Since we get 0 when we multiply a, b, and c together, we know one of them must be 0
    1. Multiplying by 0 makes the whole expression equal 0
    1. If we put 0 in for a, b or c in our equation, it will make a true statement, since the result will be 0
    1. Here our factors are x and x+2, since that's what we're multiplying together
    1. Since we're multiplying and we get a result of 0, we can use the zero product property
    1. So we know that either x is 0 or x+2 is 0
    1. Our factors are x and x+2
    2. So x=0 or x+2=0
    3. Now we can solve these equations to find our solutions
    1. Our first equation is x=0
    2. Since we already have x by itself, we don't need to do anything else
    1. Our second equation is x+2=0
    2. Subtract 2 from both sides to get x by itself
    3. x+2-2=x on the left
    4. 0-2=-2 on the right
    5. So the solution to our second equation is x=-2
    1. If we put either of these numbers in for x in our original equation, the result would be 0 and we'd get a true statement
    1. Factors are just things that are being multiplied
    2. To use the zero product property you need things being multiplied to give you a result of 0
    1. Separate out everything that is being multiplied by something else
    2. Set each of these equal to 0
    3. Solve each equation to get all the possible solutions