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The following is obtained from testing each candidates: Now, all the candidates need to be tested to see if they are a solution. Therefore, dividing each divider of \(c = 1\) by each divider of \(a = 4\), we find the following list of candidates to be factors: Now, we need to find the integer numbers that divide \(a\) and \(c\), that will be used to construct our candidates to be factors. In this case, we have that the equation we need to try to factor is \(\displaystyle 4x^2+4x+1 = 0\), which implies that corresponding coefficients are: We need to try to solve the following given quadratic equation \(\displaystyle 4x^2+4x+1=0\) by factoring. Solve the following equation by factoring \(4x^2 + 4x + 1 = 0\) Often times you will use factoring within an equation not necessarily to solve the equation, but rather to group terms. Why would care about factoring quadratic fractions?įactoring plays a very important role in different contexts, and ultimately, solving a general quadratic equation relies on a sophisticated and Now, regardless of its limitations, the solving quadratic equations with factoring is a good and quick alternative when the roots to the equation are In other words, there is not a simpleįormula for factoring, you rather follow a guessing process. The limitation of this method is that you may not be able to guess the solutions, as the solutions may not be rational.
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