what is the remainder when $(3x^3 - 2x^2 + 4x - 3)$ is divided by $(x^2 + 3x + 3)$?

- 30
- $3x - 11$
- $28x - 36$
- $28x + 30$

Question

what is the remainder when $(3x^3 - 2x^2 + 4x - 3)$ is divided by $(x^2 + 3x + 3)$?

- 30
- $3x - 11$
- $28x - 36$
- $28x + 30$

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": [ "Polynomial Division" ], "new_concepts": [], "current_concepts": [ "Polynomial Division" ] } ## Set up the polynomial long division Using the *Polynomial Division* knowledge point $$ \begin{aligned} &\text{Dividend: } 3x^3 - 2x^2 + 4x - 3 \ &\text{Divisor: } x^2 + 3x + 3 \end{aligned} $$ ## Divide the leading terms Using the *Polynomial Division* knowledge point $$ \begin{aligned} &\text{First term of quotient: } \frac{3x^3}{x^2} = 3x \ &\text{Multiply: } 3x(x^2 + 3x + 3) = 3x^3 + 9x^2 + 9x \ &\text{Subtract: } (3x^3 - 2x^2 + 4x - 3) - (3x^3 + 9x^2 + 9x) = -11x^2 - 5x - 3 \end{aligned} $$ ## Divide the next term Using the *Polynomial Division* knowledge point $$ \begin{aligned} &\text{Second term of quotient: } \frac{-11x^2}{x^2} = -11 \ &\text{Multiply: } -11(x^2 + 3x + 3) = -11x^2 - 33x - 33 \ &\text{Subtract: } (-11x^2 - 5x - 3) - (-11x^2 - 33x - 33) = 28x + 30 \end{aligned} $$

(A) 30

(B) $3x - 11$

(C) $28x - 30$

(D) $28x + 30$

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

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QUESTION IMAGE

Question

Explanation:

Set up the polynomial long division

Divide the leading terms

Divide the next term

Answer: