the product of a binomial and a trinomial is $x^3 + 3x^2 - x + 2x^2 + 6x - 2$. which expression is equivalent to this product after it has been fully simplified?

$x^3 + 5x^2 + 5x - 2$
$x^3 + 2x^2 + 8x - 2$
$x^3 + 11x^2 - 2$
$x^3 + 10x^2 - 2$

Question

the product of a binomial and a trinomial is $x^3 + 3x^2 - x + 2x^2 + 6x - 2$. which expression is equivalent to this product after it has been fully simplified?

$x^3 + 5x^2 + 5x - 2$
$x^3 + 2x^2 + 8x - 2$
$x^3 + 11x^2 - 2$
$x^3 + 10x^2 - 2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Algebraic Simplification" ], "new_concepts": [], "current_concepts": [ "Algebraic Simplification", "Polynomial Multiplication" ] } ## Identify and group like terms $$ (x^3) + (3x^2 + 2x^2) + (-x + 6x) - 2 $$ ## Combine coefficients of like terms $$ \begin{aligned} 3x^2 + 2x^2 &= 5x^2 \ -x + 6x &= 5x \end{aligned} $$ ## Write the fully simplified polynomial $$ x^3 + 5x^2 + 5x - 2 $$

(A) $x^3 + 5x^2 + 5x - 2$

(B) $x^3 + 2x^2 + 8x - 2$

(C) $x^3 + 11x^2 - 2$

(D) $x^3 + 10x^2 - 2$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Algebraic Simplification" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify and group like terms

Combine coefficients of like terms

Write the fully simplified polynomial

Answer: