Thus, (x + 2) and (x + 6) are the factors of x 2 + 8x + 12 = 0 Taking the common factor (x + 6) out, we have Hence, we split the middle term and write the quadratic equation as: ![]() Now, we can see that the factor pair (2, 6) satisfies our purpose as the sum of 6 and 2 is 8 and the product is 12. Split the middle term 8x in such a way that the factors of the product of 1 and 12 add up to make 8. We determine the factor pairs of the product of a and c such that their sum is equal to b. We split the middle term b of the quadratic equation ax 2 + bx + c = 0 when we try to factorize quadratic equations. The product of the roots in the quadratic equation ax 2 + bx + c = 0 is given by \(\alpha\beta\) = c/a.The sum of the roots of the quadratic equation ax 2 + bx + c = 0 is given by \(\alpha + \beta\) = -b/a.Splitting the Middle Term for Factoring Quadratics Thus 3x 2 + 6x = 0 is factorized as 3x(x + 2) = 0.The algebraic common factor is x in both terms.The numerical factor is 3 (coefficient of x 2) in both terms. ![]() Let us solve an example to understand the factoring quadratic equations by taking the GCD out.Ĭonsider this quadratic equation: 3x 2 + 6x = 0
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