For which values of x is the expression undefined? (8x+64)/(x^(2)-4x-12)

Identify Undefined Values: To determine when the expression is undefined, we need to find the values of x that make the denominator equal to zero, since division by zero is undefined.Factor Quadratic Expression: The denominator of the expression is x^2 - 4x - 12. We need to factor this quadratic expression to find its roots.Find Root Values: Factoring the quadratic expression, we look for two numbers that multiply to -12 and add up to -4. These numbers are -6 and +2.Factorize Expression: We can now factor the quadratic expression as (x - 6)(x + 2).Set Factors Equal: Setting each factor equal to zero gives us the potential values for x that would make the denominator zero. So we have x - 6 = 0 and x + 2 = 0.Solve for x: Solving x - 6 = 0 gives us x = 6.Values Making Expression Undefined: Solving x + 2 = 0 gives us x = -2.The values of x that make the expression undefined are x = 6 and x = -2, because these values make the denominator zero.

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For which values of $x$ is the expression undefined? $\newline$ $\frac{8x+64}{x^{2}-4x-12}$

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Algebra 1

Evaluate integers raised to rational exponents

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Q. For which values of

x

is the expression undefined?

\newline

\frac{8x+64}{x^{2}-4x-12}

Identify Undefined Values: To determine when the expression is undefined, we need to find the values of $x$ that make the denominator equal to $0$ , since division by $0$ is undefined.
Factor Quadratic Expression: The denominator of the expression is $x^2 - 4x - 12$ . We need to factor this quadratic expression to find its roots.
Find Root Values: Factoring the quadratic expression, we look for two numbers that multiply to $-12$ and add up to $-4$ . These numbers are $-6$ and $+2$ .
Factorize Expression: We can now factor the quadratic expression as $(x - 6)(x + 2)$ .
Set Factors Equal: Setting each factor equal to zero gives us the potential values for $x$ that would make the denominator zero. So we have $x - 6 = 0$ and $x + 2 = 0$ .
Solve for x: Solving $x - 6 = 0$ gives us $x = 6$ .
Values Making Expression Undefined: Solving $x + 2 = 0$ gives us $x = -2$ .
Values Making Expression Undefined: Solving $x + 2 = 0$ gives us $x = -2$ .The values of $x$ that make the expression undefined are $x = 6$ and $x = -2$ , because these values make the denominator zero.