What value would cause the rational expression 5x+15/-2x^2-16x-32 to be undefined?
The rational expression 5x+15/-2x^2-16x-32 would be undefined when the denominator, -2x^2-16x-32, is equal to zero.
To find the value(s) that make the denominator zero, we can solve the quadratic equation -2x^2-16x-32 = 0.
First, let's divide the equation by -2 to simplify it: x^2 + 8x + 16 = 0.
Now, we can factor this quadratic equation: (x + 4)(x + 4) = 0.
This equation has a double root of -4, meaning that the expression would be undefined when x = -4.
To find the value that would cause the rational expression 5x + 15 / -2x^2 - 16x - 32 to be undefined, we need to identify any values of x that would make the denominator equal to zero. A rational expression is undefined when the denominator is zero because division by zero is undefined in mathematics.
In this case, the denominator is -2x^2 - 16x - 32. To determine when it equals zero, we can set it equal to zero and solve for x:
-2x^2 - 16x - 32 = 0
We can divide both sides of the equation by -2 to simplify:
x^2 + 8x + 16 = 0
Now, we can factor the quadratic equation:
(x + 4)(x + 4) = 0
This gives us a repeated root of x = -4.
Therefore, the value that would cause the rational expression 5x + 15 / -2x^2 - 16x - 32 to be undefined is x = -4.
To determine the value that would cause the rational expression 5x + 15 / -2x^2 - 16x - 32 to be undefined, we need to identify any values of x that would make the denominator equal to zero.
In this case, the denominator is -2x^2 - 16x - 32. To find the values of x that make the denominator zero, we need to set the denominator equal to zero and solve for x.
-2x^2 - 16x - 32 = 0
To simplify this equation, we can first divide both sides by -2.
x^2 + 8x + 16 = 0
Next, we can factor the quadratic equation:
(x + 4)(x + 4) = 0
The factored form of the equation tells us that x = -4.
Therefore, the value -4 would cause the rational expression 5x + 15 / -2x^2 - 16x - 32 to be undefined.