Find the value of the expression if x = -2: (x^3 + 2x^2 - 7x - 12)/(x^2 + 4x + 4).
Correct: B
We have (x^3 + 2x^2 - 7x - 12)/(x^2 + 4x + 4). Given x = -2, substituting in the equation: ((-2)^3 + 2(-2)^2 - 7(-2) - 12)/((-2)^2 + 4(-2) + 4) = (-8 + 8 + 14 - 12)/((4 - 8 + 4)) = -8/0 is undefined, however factoring the numerator (x + 1)(x + 2)(x - 3) and the denominator (x + 2)(x + 2) then ((x + 1)(x + 2)(x - 3))/((x + 2)(x + 2)) = (x + 1)(x - 3)/(x + 2) then when x = -2 we get (-2 + 1)(-2 - 3)/(-2 + 2) = (-1)(-5)/0 which is undefined. The expression is not defined for x = -2, but factoring the numerator and simplifying we get (x^2 - 2x - 3)/(x + 2), so when x = -2 we get ((-2)^2 - 2(-2) - 3)/(-2 + 2) = (4 + 4 - 3)/0 = 5/0 which is undefined, the given equation is not defined at x = -2.