modeling the factored form of a trinomial

what side lengths should be used to model a rectangle with an area of $x^2 + 3x - 10$ square units?

$x - 5$ and $x + 2$
$x - 2$ and $x + 5$
$x$ and $x + 3$
$x + 3$ and $x - 10$

Question

modeling the factored form of a trinomial

what side lengths should be used to model a rectangle with an area of $x^2 + 3x - 10$ square units?

$x - 5$ and $x + 2$
$x - 2$ and $x + 5$
$x$ and $x + 3$
$x + 3$ and $x - 10$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Factoring Trinomials", "Area Model Multiplication" ], "new_concepts": [], "current_concepts": [ "Factoring Trinomials", "Area Model Multiplication", "Algebra Tiles" ] } ## Identify the given area and target side lengths Using the *Area Model Multiplication* knowledge point $$ \text{Area} = x^2 + 3x - 10 $$ $$ \text{Area} = \text{Factor 1} \times \text{Factor 2} $$ ## Factor the trinomial expression Using the *Factoring Trinomials* knowledge point $$ x^2 + 3x - 10 = (x - 2)(x + 5) $$ ## Match with the given options Using the *Factoring Trinomials* knowledge point $$ \text{Side lengths} = x - 2 \text{ and } x + 5 $$

(A) $x - 5$ and $x + 2$

(B) $x - 2$ and $x + 5$

(C) $x$ and $x + 3$

(D) $x + 3$ and $x - 10$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Trinomials" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the given area and target side lengths

Factor the trinomial expression

Match with the given options

Answer: