the volume of the cereal box must be $192\text{ in.}^3$.

height: $(x + 10)\text{ in.}$
width: $(x - 4)\text{ in.}$
length: $x\text{ in.}$

polynomial equation: $x^3 + 6x^2 - 40x = 192$
solutions: $x = -8$, $x = -4$, and $x = 6$

in the context of this problem, which solutions to the polynomial equation can you eliminate because they do not make sense?

$x = -8$
$x = -4$
$x = 6$

Question

the volume of the cereal box must be $192\text{ in.}^3$.

height: $(x + 10)\text{ in.}$
width: $(x - 4)\text{ in.}$
length: $x\text{ in.}$

polynomial equation: $x^3 + 6x^2 - 40x = 192$
solutions: $x = -8$, $x = -4$, and $x = 6$

in the context of this problem, which solutions to the polynomial equation can you eliminate because they do not make sense?

$x = -8$
  $x = -4$
  $x = 6$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Polynomial Word Problems", "Extraneous Solutions" ], "current_concepts": [ "Polynomial Word Problems", "Extraneous Solutions", "Polynomial Roots" ] } ## Analyze physical constraints on dimensions $$ \begin{aligned} &\text{Length: } x > 0 \ &\text{Width: } x - 4 > 0 \implies x > 4 \ &\text{Height: } x + 10 > 0 \implies x > -10 \ &\text{Combined constraint: } x > 4 \end{aligned} $$ ## Evaluate given solutions against constraints $$ \begin{aligned} &x = -8: \quad -8 \le 4 \quad (\text{Invalidates length and width}) \ &x = -4: \quad -4 \le 4 \quad (\text{Invalidates length and width}) \ &x = 6: \quad 6 > 4 \quad (\text{Valid}) \end{aligned} $$ ## Identify solutions to eliminate $$ x = -8, \quad x = -4 $$

x = -8

x = -4

x = 6

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Word Problems" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Analyze physical constraints on dimensions

Evaluate given solutions against constraints

Identify solutions to eliminate

Answer: