How to Factor Quadratic Equations for Algebra I
Factoring quadratics can get confusing and difficult, especially when the question gets complicated with additional variables. Math problems, however, are all to be taken step by step. To show how to simplify and factor quadratic equations step-by-step, I will be using an example problem: 3x2 +30 -7x +x4 = 2x2 +3x +x4 +6.
At a first glance, this problem looks confusing, but it’s like any other quadratic problem. The first step is to make the equation equal to zero. In order to do so, we want to bring all the variables and numbers to one side of the equation. As a result we will get: 3x2 +30 -7x +x4 -2x2 -3x -x4 -6 = 0.
Now we want to organize highest power to lowest power: x4 –x4 +3x2 -2x2 -7x -3x +30 -6 = 0. Next step is to simplify by combining like terms to get: x2 -10x +24 = 0. Next step is to factor. Since the coefficient of x2 is 1, we know that it is 1x times 1x.
So, it’ll be (x )(x ). Then, we want to find the signs and numbers that go in each parenthesis. Because we know that it is positive 24, we know that (-)(-) = (+) and (+)(+) = (+). But since it is negative 10x, we know that it must be two negatives: (x - )(x - ). Now, we want to find factors of 24, which add up to -10. We have the following factors: Possible factors -1, -24 -2, -12 -3, -8 -4, -6 Sums of factors -25 -14 -11 -10 So we know that the answer is (x -4)(x -6) = 0.
Final step, solve individually: x – 4 = 0 x – 6 = 0 x = 4 x = 6 You can check your answers by plugging those values back into the original problem. Hope that helped! Good luck!