factor the trinomial, if possible.

\10x^2 - 7x - 3\

not factorable

Question

factor the trinomial, if possible.

\10x^2 - 7x - 3\

not factorable

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Factoring Trinomials", "Trinomial Factoring by Grouping", "Finding Factors with Given Sum and Product" ], "new_concepts": [], "current_concepts": [ "Factoring Trinomials", "Trinomial Factoring by Grouping", "Finding Factors with Given Sum and Product" ] } ## Identify coefficients of the trinomial Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &ax^2 + bx + c = 10x^2 - 7x - 3\ &a = 10,\quad b = -7,\quad c = -3 \end{aligned} $$ ## Find factors with given sum and product Using the *Finding Factors with Given Sum and Product* knowledge point $$ \begin{aligned} &\text{Product } (ac) = 10 \times (-3) = -30\ &\text{Sum } (b) = -7\ &\text{Factors of } -30 \text{ that sum to } -7 \text{ are } -10 \text{ and } 3 \end{aligned} $$ ## Rewrite and factor by grouping Using the *Trinomial Factoring by Grouping* knowledge point $$ \begin{aligned} 10x^2 - 7x - 3 &= 10x^2 - 10x + 3x - 3\ &= 10x(x - 1) + 3(x - 1)\ &= (10x + 3)(x - 1) \end{aligned} $$ Factor the trinomial, if possible. $10x^2 - 7x - 3 =$ $(10x + 3)(x - 1)$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Trinomials" ] }

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QUESTION IMAGE

Question

Explanation:

Identify coefficients of the trinomial

Find factors with given sum and product

Rewrite and factor by grouping

Answer: