A. -8 only B. -8 and 4 C. 4 and 8 D. -8 and -4 E. -4 only
(D) A fraction is undefined when its denominator is equal to zero. So the question is really asking us to solve the quadratic equation x² + 12x + 32 = 0.
The first step in solving the quadratic equation is to factor it into: (x + 8)(x + 4) = 0.
The product of two numbers equals zero if at least one of the factors is zero. So we set each factor equal to zero and solve: (x + 8) = 0 or (x + 4) = 0 x = -8 or -4.
So if x is either -8 or -4, the denominator will be zero. Therefore these both numbers will make the fraction undefined.
The correct answer is choice (D). If you have trouble factoring the denominator, you can also backsolve a problem like this. You should substitute the values in the answer choices into the denominator to see which number(s) make(s) the denominator zero. ---------- Why didn't you verify that the numerator does not equal zero? A fraction is only undefined if N/0 not 0/0.
The division by 0 is undefined irregardless of what the numerator is. 0/0 is still UNDEFINED.
Note, that the fraction
(x + 3)(x + 1) (x + 3)(x + 2)
is undefined when x = -2 or x = -3, in spite of the fact that (x + 3) is in the both: denominator and numerator. We can NOT simplify the fraction in this case, because the original fraction results in 0/0 when x = -3, which is undefined, while the simplified fraction yields 2 for x = -3.
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