What are the excluded values of the product
14x

x+2
⋅
x

x2+3x+2
? Select all that apply.

Question

What are the excluded values of the product 
14x

x+2
⋅
x

x2+3x+2
 ? Select all that apply.

BlackTom AI · Accepted Answer

Consider the expression in the problem: we are asked for the values of x that are excluded because they make a denominator zero in the product.
Option 1: x = -2. Here, the denominators include (x+2) and (x^2+3x+2). Substituting x = -2 makes (x+2) = 0 and also x^2+3x+2 = (-2)^2 + 3(-2) + 2 = 4 - 6 + 2 = 0, so the expression is undefined. Therefore, x = -2 is an excluded value.
Option 2: x = -1. This value makes the factor (x^2+3x+2) = (x+1)(x+2) equal to zero, since (-1)^2 + 3(-1) + 2 = 1 - 3 + 2 = 0 and also explicitly (x+1) at x = -1 is zero. Thus the product is undefined at x = -1, so x = -1 is also an excluded value.
In summary, the expression has denominators that vanish at x = -2 and x = -1, making both values excluded. Neither value cancels out in the numerator to permit a simplification, so they remain excluded for the defined domain of the expression.

ALGII141-027 5.2 Practice Problems

What are the excluded values of the product 14x x+2 ⋅ x x2+3x+2 ? Select all that apply.

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