Advanced Polynomial Equations
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Students learn that when solving a polynomial equation such as (x + 1)(x - 8) = 10, the equation cannot be split up into two separate equations as a first step, because it is not set equal to zero. So the first step in this problem is to F.O.I.L. on the left side of the equation to get x^2 - 7x - 8 = 10, then subtract 10 from both sides to get x^2 - 7x - 18 = 0, then factor the left side to get (x - 9)(x + 2) = 0, then split things up into two separate equations: x - 9 = 0 and x + 2 = 0, and solve each equation from here to get x = 9 or x = -2.