what is the quotient of this expression?
\frac{x^4 - 3x^3 + 2x^2 - 5x + 1}{x^2 - 5}
select the correct answer. for help, see this worked example.

- $x^2 - 3x - 7 - \frac{20x - 34}{x^2 - 5}$
- $x^2 - 3x + 7 - \frac{20x + 36}{x^2 - 5}$
- $x^2 - 3x + 7 - \frac{20x - 36}{x^2 - 5}$
- $x^2 - 3x - 7 - \frac{20x + 34}{x^2 - 5}$

Question

what is the quotient of this expression?
\frac{x^4 - 3x^3 + 2x^2 - 5x + 1}{x^2 - 5}
select the correct answer. for help, see this worked example.

- $x^2 - 3x - 7 - \frac{20x - 34}{x^2 - 5}$
- $x^2 - 3x + 7 - \frac{20x + 36}{x^2 - 5}$
- $x^2 - 3x + 7 - \frac{20x - 36}{x^2 - 5}$
- $x^2 - 3x - 7 - \frac{20x + 34}{x^2 - 5}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Long Division" ], "new_concepts": [], "current_concepts": [ "Polynomial Long Division" ] } ## Set up the polynomial division $$ (x^4 - 3x^3 + 2x^2 - 5x + 1) \div (x^2 - 5) $$ ## Perform division steps $$ \begin{array}{r|l} \text{Divide } x^4 \text{ by } x^2: & x^2 \ \text{Multiply } x^2(x^2 - 5): & x^4 - 5x^2 \ \text{Subtract from dividend}: & (x^4 - 3x^3 + 2x^2) - (x^4 - 5x^2) = -3x^3 + 7x^2 \ \text{Bring down next term}: & -3x^3 + 7x^2 - 5x \ \hline \text{Divide } -3x^3 \text{ by } x^2: & -3x \ \text{Multiply } -3x(x^2 - 5): & -3x^3 + 15x \ \text{Subtract}: & (-3x^3 + 7x^2 - 5x) - (-3x^3 + 15x) = 7x^2 - 20x \ \text{Bring down next term}: & 7x^2 - 20x + 1 \ \hline \text{Divide } 7x^2 \text{ by } x^2: & +7 \ \text{Multiply } 7(x^2 - 5): & 7x^2 - 35 \ \text{Subtract}: & (7x^2 - 20x + 1) - (7x^2 - 35) = -20x + 36 \end{array} $$ ## Write final expression $$ x^2 - 3x + 7 + \frac{-20x + 36}{x^2 - 5} = x^2 - 3x + 7 - \frac{20x - 36}{x^2 - 5} $$

(A) $x^2 - 3x - 7 - \frac{20x - 34}{x^2 - 5}$

(B) $x^2 - 3x + 7 - \frac{20x + 36}{x^2 - 5}$

(C) $x^2 - 3x + 7 - \frac{20x - 36}{x^2 - 5}$

(D) $x^2 - 3x - 7 - \frac{20x + 34}{x^2 - 5}$

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

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QUESTION IMAGE

Question

Explanation:

Set up the polynomial division

Perform division steps

Write final expression

Answer: