select the correct answer.

one factor of the polynomial (3x^3 + 20x^2 - 21x + 88) is ((x + 8)). what is the other factor of the polynomial? (note: use long division.)

(a) ((3x^2 - 4x + 11))
(b) ((3x^2 - 4x))
(c) ((3x^2 + 11))
(d) ((3x^2 + 4x - 11))

Question

select the correct answer.

one factor of the polynomial (3x^3 + 20x^2 - 21x + 88) is ((x + 8)). what is the other factor of the polynomial? (note: use long division.)

(a) ((3x^2 - 4x + 11))
(b) ((3x^2 - 4x))
(c) ((3x^2 + 11))
(d) ((3x^2 + 4x - 11))

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", "Polynomial Factoring" ] } ## Set up the polynomial division $$ (3x^3 + 20x^2 - 21x + 88) \div (x + 8) $$ ## Perform the division steps $$ \begin{array}{r|l} \text{Divide } 3x^3 \text{ by } x: & 3x^2 \ \text{Multiply } 3x^2(x + 8): & 3x^3 + 24x^2 \ \text{Subtract from dividend}: & (3x^3 + 20x^2) - (3x^3 + 24x^2) = -4x^2 \ \text{Bring down next term}: & -4x^2 - 21x \ \text{Divide } -4x^2 \text{ by } x: & -4x \ \text{Multiply } -4x(x + 8): & -4x^2 - 32x \ \text{Subtract}: & (-4x^2 - 21x) - (-4x^2 - 32x) = 11x \ \text{Bring down next term}: & 11x + 88 \ \text{Divide } 11x \text{ by } x: & 11 \ \text{Multiply } 11(x + 8): & 11x + 88 \ \text{Subtract}: & (11x + 88) - (11x + 88) = 0 \end{array} $$ ## Identify the quotient factor $$ 3x^2 - 4x + 11 $$

(3x^2 - 4x + 11)

(3x^2 - 4x)

(3x^2 + 11)

(3x^2 + 4x - 11)

{ "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 the division steps

Identify the quotient factor

Answer: