Algebra: Chapter 6, Lesson 8, page 286.
Solving Equations by Factoring
The principle of zero products states that: for any rational numbers a and b, if the product `ab = 0`, then `a=0` or `b=0` or both `a` and `b = 0`.
Factor and solve equations by using the following:
- Get `0` on one side of the equation using the addition property
- FACTOR the expression on the other side of the equation
- Set each factor equal to zero
- Solve each equation.
If we have an equation with `0` on one side and a factorization on the other side, we can solve the equation by finding the values that make the factors `0`. This is even easier!
Since we are solving quadratic equations (they are NOT linear because they have an exponent that is squared, `x^2`), we can have at MOST 2 solutions. We can have NO solutions, 1 solution or 2 solutions.
Remember to use all the techniques you know to factor!