The quadratic formula will always get you the two roots. From there, you can get the factored form if you remember that both factors are really equal to zero.Here is an example:x^2 + 2x - 8set the expression equal to zerox^2 +2x - 8 = 0pull out that quadratic formulaa = 1, b = 2, c = -8x = (-(2) ± √((2)^2 - 4(1)(-8))) / 2(1)x = (-2 + √36) / 2 OR x = (-2 - √36) / 2x = 2 OR x = -4Now...take those two "solutions" and solve the equations for zero. I know it sounds weird, but trust me.x = 2 → x - 2 = 0 → one of the factors is (x - 2)x = -4 → x + 4 = 0 → the other factor is (x + 4)So...x^2 + 2x - 8 is equivalent to (x - 2)(x + 4)This was an "easier" example, but this method always works!
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