select the correct answer.

using synthetic division, what is the factored form of this polynomial?
\x^4 + 6x^3 + 33x^2 + 150x + 200\

$(x - 2)(x - 4)(x - 5)(x + 5)$
$(x - 2)(x - 4)(x^2 + 25)$
$(x + 2)(x + 4)(x^2 + 25)$
$(x + 2)(x + 4)(x - 5)(x + 5)$

Question

select the correct answer.

using synthetic division, what is the factored form of this polynomial?
\x^4 + 6x^3 + 33x^2 + 150x + 200\

$(x - 2)(x - 4)(x - 5)(x + 5)$
$(x - 2)(x - 4)(x^2 + 25)$
$(x + 2)(x + 4)(x^2 + 25)$
$(x + 2)(x + 4)(x - 5)(x + 5)$

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", "Polynomial Factoring" ], "new_concepts": [], "current_concepts": [ "Synthetic Division", "Polynomial Factoring" ] } ## Test potential rational roots using synthetic division $$ \begin{aligned} &\text{For } x = -2:\ &\begin{array}{r|rrrrr} -2 & 1 & 6 & 33 & 150 & 200 \ & & -2 & -8 & -50 & -200 \ \hline & 1 & 4 & 25 & 100 & 0 \end{array}\ &\text{Thus, } (x + 2) \text{ is a factor, leaving } x^3 + 4x^2 + 25x + 100. \end{aligned} $$ ## Factor the remaining cubic polynomial $$ \begin{aligned} &\text{For } x = -4 \text{ on } x^3 + 4x^2 + 25x + 100:\ &\begin{array}{r|rrrr} -4 & 1 & 4 & 25 & 100 \ & & -4 & 0 & -100 \ \hline & 1 & 0 & 25 & 0 \end{array}\ &\text{Thus, } (x + 4) \text{ is a factor, leaving } x^2 + 25. \end{aligned} $$ ## Write the complete factored form $$ (x + 2)(x + 4)(x^2 + 25) $$

(A) $(x - 2)(x - 4)(x - 5)(x + 5)$

(B) $(x - 2)(x - 4)(x^2 + 25)$

(C) $(x + 2)(x + 4)(x^2 + 25)$

(D) $(x + 2)(x + 4)(x - 5)(x + 5)$

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

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QUESTION IMAGE

Question

Explanation:

Test potential rational roots using synthetic division

Factor the remaining cubic polynomial

Write the complete factored form

Answer: