Math Tutoring on Solving Quadratic Equations by Factoring
A "quadratic” is a polynomial that looks like ax² + bx + c, where a, b and c are just numbers. The method for solving quadratic equations by factoring is based upon the zero factor property of real numbers. Here is what it says, “if two numbers, a and b, are multiplied together and the resulting product is zero, then at least one of the numbers must be zero.” So if we have a x b = 0 then a = 0 or b = 0 or they both = 0. Let us go ahead and apply this to quadratic equations. So all of these problems will be factorable, remember the first step in factoring is to look for the greatest common factor and there is a common factor of x here. So let us go ahead and factor x out. For the easy case of factoring, you will find two numbers that will not only multiply to equal the constant term "c", but also add up to equal "b", the coefficient on the x-term. In some cases, there is not a GCF for all the terms in a polynomial. If four terms have no GCF, then factoring by grouping is applied and following are the steps:
Step 1: Group the first two terms together and then the last two terms together.
Step 2: Factor out a GCF from each separate binomial.
Step 3: Factor out the common binomial.
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1. What is a quadratic equation?
3. How do you find the factors of an equation?
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