using synthetic division, find $(2x^4 + 4x^3 + 2x^2 + 8x + 8) \div (x + 2)$.

$2x^3 + 2x + 4$

$2x^4 + 2x^2 + 4x$

$2x^3 + 2x + 4 + \frac{1}{x + 2}$

$2x^3 + 2x^2 + 4$

Question

using synthetic division, find $(2x^4 + 4x^3 + 2x^2 + 8x + 8) \div (x + 2)$.

$2x^3 + 2x + 4$

$2x^4 + 2x^2 + 4x$

$2x^3 + 2x + 4 + \frac{1}{x + 2}$

$2x^3 + 2x^2 + 4$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Synthetic Division" ], "new_concepts": [], "current_concepts": [ "Synthetic Division", "Polynomial Long Division" ] } ## Set up the synthetic division $$ \begin{array}{r|rrrrr} -2 & 2 & 4 & 2 & 8 & 8 \ & & -4 & 0 & -4 & -8 \ \hline & 2 & 0 & 2 & 4 & 0 \end{array} $$ ## Interpret the quotient and remainder $$ \begin{aligned} \text{Quotient} &= 2x^3 + 0x^2 + 2x + 4 \ &= 2x^3 + 2x + 4 \ \text{Remainder} &= 0 \end{aligned} $$ ## Match with the given options $$ (2x^4 + 4x^3 + 2x^2 + 8x + 8) \div (x + 2) = 2x^3 + 2x + 4 $$

(A) $2x^3 + 2x + 4$

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

(C) $2x^3 + 2x + 4 + \frac{1}{x+2}$

(D) $2x^3 + 2x^2 + 4$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Set up the synthetic division

Interpret the quotient and remainder

Match with the given options

Answer: