Factoring can be a quick and effective method for finding the rational solutions to a quadratic equation. This lesson assumes that you already know methods for factoring quadratic expressions including ones with leading coefficients other than one. We are now going to apply these methods to solve equations. It should be noted that not all quadratic equations are factorable; if a quadratic is not factorable then the solution are either irrational or complex numbers.
In order to solve by factoring we need one of side of the equation to equal zero, the other side should be a quadratic expression in standard form. Then we need to apply the Zero Product Property which states if a product is equal to zero then at least one of its factors must be zero.
In this video Sal Khan of Khan Academy goes through the entire process in detail:
Here is a link to the entire lesson on Khan Academy which you should explore if you want to examples or explanation.
A lot of students find factoring alone be challenging enough without adding the element of solving the equation. Thankfully we've seen that once you have the quadratic factored, solving the equation is fairly easy. Here are some resources and practice with factoring.
Factoring and Zero
Factoring can be a quick and effective method for finding the rational solutions to a quadratic equation. This lesson assumes that you already know methods for factoring quadratic expressions including ones with leading coefficients other than one. We are now going to apply these methods to solve equations. It should be noted that not all quadratic equations are factorable; if a quadratic is not factorable then the solution are either irrational or complex numbers.
In order to solve by factoring we need one of side of the equation to equal zero, the other side should be a quadratic expression in standard form. Then we need to apply the Zero Product Property which states if a product is equal to zero then at least one of its factors must be zero.
In this video Sal Khan of Khan Academy goes through the entire process in detail:
Here is a link to the entire lesson on Khan Academy which you should explore if you want to examples or explanation.
Skills Practice:
Need some extra help with factoring?
A lot of students find factoring alone be challenging enough without adding the element of solving the equation. Thankfully we've seen that once you have the quadratic factored, solving the equation is fairly easy. Here are some resources and practice with factoring.