7.2 adding & subtracting polynomials quiz

simplify: $(6x^2 - 2x + 1) - (4x^2 + 5x - 3)$

$\bigcirc 10^2 - 3x - 2$
$\bigcirc 2x^2 - 3x + 4$
$\bigcirc 2x^2 + 3x - 2$
$\bigcirc 2x^2 - 7x + 4$

Question

7.2 adding & subtracting polynomials quiz

simplify: $(6x^2 - 2x + 1) - (4x^2 + 5x - 3)$

$\bigcirc 10^2 - 3x - 2$
$\bigcirc 2x^2 - 3x + 4$
$\bigcirc 2x^2 + 3x - 2$
$\bigcirc 2x^2 - 7x + 4$

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": [ "Subtracting Polynomials", "Distributive Property", "Combining Like Terms" ], "new_concepts": [], "current_concepts": [ "Subtracting Polynomials", "Distributive Property", "Combining Like Terms" ] } ## Distribute the negative sign Using the *Distributive Property* and *Subtracting Polynomials* knowledge points $$ \begin{aligned} -(4x^2 + 5x - 3) = -4x^2 - 5x + 3 \end{aligned} $$ ## Rewrite the expression Using the *Subtracting Polynomials* knowledge point $$ (6x^2 - 2x + 1) - (4x^2 + 5x - 3) = 6x^2 - 2x + 1 - 4x^2 - 5x + 3 $$ ## Group like terms Using the *Combining Like Terms* knowledge point $$ (6x^2 - 4x^2) + (-2x - 5x) + (1 + 3) $$ ## Combine the coefficients Using the *Combining Like Terms* knowledge point $$ \begin{aligned} &6x^2 - 4x^2 = 2x^2\ &-2x - 5x = -7x\ &1 + 3 = 4\ &\text{Result: } 2x^2 - 7x + 4 \end{aligned} $$

(A) $10^2 - 3x - 2$

(B) $2x^2 - 3x + 4$

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

(D) $2x^2 - 7x + 4$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Subtracting Polynomials" ] }

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QUESTION IMAGE

Question

Explanation:

Distribute the negative sign

Rewrite the expression

Group like terms

Combine the coefficients

Answer: