question 1
evaluate the polynomial $3x^2 - 2x + 5$ when $x = 4$

question 2
evaluate the polynomial $x^3 + 2x^2 - 8x - 2$ when $x = -2$

question 3
combine like terms: $4x^3 + 9x^3$

Question

question 1
evaluate the polynomial $3x^2 - 2x + 5$ when $x = 4$

question 2
evaluate the polynomial $x^3 + 2x^2 - 8x - 2$ when $x = -2$

question 3
combine like terms: $4x^3 + 9x^3$

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Polynomial Evaluation", "Combining Like Terms" ], "current_concepts": [ "Polynomial Evaluation", "Combining Like Terms" ] } ## Evaluate the first polynomial $$ \begin{aligned} &P(x) = 3x^2 - 2x + 5,\quad x = 4\ &P(4) = 3(4)^2 - 2(4) + 5\ &P(4) = 3(16) - 8 + 5\ &P(4) = 48 - 8 + 5 = 45 \end{aligned} $$ ## Evaluate the second polynomial $$ \begin{aligned} &Q(x) = x^3 + 2x^2 - 8x - 2,\quad x = -2\ &Q(-2) = (-2)^3 + 2(-2)^2 - 8(-2) - 2\ &Q(-2) = -8 + 2(4) + 16 - 2\ &Q(-2) = -8 + 8 + 16 - 2 = 14 \end{aligned} $$ ## Combine like terms $$ \begin{aligned} &4x^3 + 9x^3\ &(4 + 9)x^3 = 13x^3 \end{aligned} $$ ## Question 1 Evaluate the polynomial $3x^2 - 2x + 5$ when $x = 4$ 45 ## Question 2 Evaluate the polynomial $x^3 + 2x^2 - 8x - 2$ when $x = -2$ 14 ## Question 3 Combine like terms: $4x^3 + 9x^3$ $13x^3$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Evaluation" ] }

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QUESTION IMAGE

Question

Explanation:

Evaluate the first polynomial

Evaluate the second polynomial

Combine like terms

Answer:

Question 1

Question 2

Question 3