select the correct answer.

what is the completely factored form of this expression?

(3x^2 - 17x - 28)

(3x + 4)(x + 7)
(3x + 4)(x - 7)
3x^2 - 17x - 28
(3x^2 + 4)(x - 7)

Question

select the correct answer.

what is the completely factored form of this expression?

(3x^2 - 17x - 28)

(3x + 4)(x + 7)
(3x + 4)(x - 7)
3x^2 - 17x - 28
(3x^2 + 4)(x - 7)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Factoring Trinomials", "Quadratic Factoring" ], "new_concepts": [], "current_concepts": [ "Factoring Trinomials", "Quadratic Factoring" ] } ## Identify the coefficients of the quadratic expression Using the *Factoring Trinomials* and *Quadratic Factoring* knowledge points $$ \begin{aligned} &a = 3 \ &b = -17 \ &c = -28 \end{aligned} $$ ## Find two numbers that multiply to ac and add to b Using the *Factoring Trinomials* and *Quadratic Factoring* knowledge points $$ \begin{aligned} &a \cdot c = 3 \cdot (-28) = -84 \ &b = -17 \ &\text{Factors of } -84 \text{ that sum to } -17: \quad -21 \text{ and } 4 \ &-21 \cdot 4 = -84 \ &-21 + 4 = -17 \end{aligned} $$ ## Rewrite and factor by grouping Using the *Factoring Trinomials* and *Quadratic Factoring* knowledge points $$ \begin{aligned} 3x^2 - 17x - 28 &= 3x^2 - 21x + 4x - 28 \ &= 3x(x - 7) + 4(x - 7) \ &= (3x + 4)(x - 7) \end{aligned} $$

(3x + 4)(x + 7)

(3x + 4)(x - 7)

3x^2 - 17x - 28

(3x^2 + 4)(x - 7)

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

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QUESTION IMAGE

Question

Explanation:

Identify the coefficients of the quadratic expression

Find two numbers that multiply to ac and add to b

Rewrite and factor by grouping

Answer: