which shows the four-term polynomial and factored form of $x^2 + 6x - 27$?

$x^2 + 3x - 9x - 27 = (x + 3)(x - 9)$
$x^2 + 6x - 3x - 27 = (x + 6)(x - 3)$
$x^2 + 9x - 3x - 27 = (x + 9)(x - 3)$
$x^2 + 3x - 6x - 27 = (x + 3)(x - 6)$

Question

which shows the four-term polynomial and factored form of $x^2 + 6x - 27$?

$x^2 + 3x - 9x - 27 = (x + 3)(x - 9)$
$x^2 + 6x - 3x - 27 = (x + 6)(x - 3)$
$x^2 + 9x - 3x - 27 = (x + 9)(x - 3)$
$x^2 + 3x - 6x - 27 = (x + 3)(x - 6)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Factoring Trinomials", "X Method Factoring" ], "new_concepts": [], "current_concepts": [ "Factoring Trinomials", "X Method Factoring", "Factoring by Grouping" ] } ## Find two numbers that multiply to -27 and add to 6 $$ \begin{aligned} &p \cdot q = -27 \ &p + q = 6 \ &\implies p = 9,\quad q = -3 \end{aligned} $$ ## Rewrite the middle term using these two numbers $$ x^2 + 6x - 27 = x^2 + 9x - 3x - 27 $$ ## Factor by grouping $$ \begin{aligned} x^2 + 9x - 3x - 27 &= x(x + 9) - 3(x + 9) \ &= (x + 9)(x - 3) \end{aligned} $$

(A) $x^2 + 3x - 9x - 27 = (x + 3)(x - 9)$

(B) $x^2 + 6x - 3x - 27 = (x + 6)(x - 3)$

(C) $x^2 + 9x - 3x - 27 = (x + 9)(x - 3)$

(D) $x^2 + 3x - 6x - 27 = (x + 3)(x - 6)$

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

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QUESTION IMAGE

Question

Explanation:

Find two numbers that multiply to -27 and add to 6

Rewrite the middle term using these two numbers

Factor by grouping

Answer: