What is the set of all values of x for which the expression
x + 6 /x2 −2x−8
is not defined?
A) {−6,−4,2} B) {−6,−2,4} C) {−4,2} D) {−2,4} E) {−6}
To determine the set of all values of x for which the expression is not defined, we need to find the values of x that make the denominator (x^2 - 2x - 8) equal to zero. This is because division by zero is undefined.
To find the values of x that make the denominator zero, we can solve the quadratic equation x^2 - 2x - 8 = 0.
To solve this quadratic equation, we can factor it:
(x - 4)(x + 2) = 0
Setting each factor equal to zero, we get:
x - 4 = 0 => x = 4
x + 2 = 0 => x = -2
Therefore, the values of x that make the denominator zero (and hence the expression undefined) are x = 4 and x = -2.
Therefore, the correct answer is D) {−2,4}.