what is the factored form of this polynomial?

\p(x) = x^3 + 7x^2 + 4x - 12\

select the correct answer from each drop-down menu. for help, see this worked example.

\p(x) = ( \text{choose an answer} )( \text{choose an answer} )( \text{choose an answer} )\

Question

what is the factored form of this polynomial?

\p(x) = x^3 + 7x^2 + 4x - 12\

select the correct answer from each drop-down menu. for help, see this worked example.

\p(x) = ( \text{choose an answer} )( \text{choose an answer} )( \text{choose an answer} )\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Factor Theorem", "Factoring Polynomials" ], "new_concepts": [], "current_concepts": [ "Factor Theorem", "Factoring Polynomials", "Polynomial Long Division" ] } ## Find a rational root using the Factor Theorem $$ \begin{aligned} &p(1) = 1^3 + 7(1)^2 + 4(1) - 12 = 1 + 7 + 4 - 12 = 0\ &\text{Thus, } (x - 1) \text{ is a factor.} \end{aligned} $$ ## Divide the polynomial by the linear factor $$ \begin{aligned} &\frac{x^3 + 7x^2 + 4x - 12}{x - 1} = x^2 + 8x + 12 \end{aligned} $$ ## Factor the remaining quadratic expression $$ \begin{aligned} &x^2 + 8x + 12 = (x + 2)(x + 6)\ &p(x) = (x - 1)(x + 2)(x + 6) \end{aligned} $$ What is the factored form of this polynomial? $p(x) = x^3 + 7x^2 + 4x - 12$ $p(x) =$ ($x - 1$)($x + 2$)($x + 6$) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Polynomials" ] }

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QUESTION IMAGE

Question

Explanation:

Find a rational root using the Factor Theorem

Divide the polynomial by the linear factor

Factor the remaining quadratic expression

Answer: