exponents and polynomials
factoring a quadratic with leading coefficient greater than 1

factor.

\2y^2 + 13y + 15\

Question

exponents and polynomials
factoring a quadratic with leading coefficient greater than 1

factor.

\2y^2 + 13y + 15\

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", "Factoring by Grouping", "AC Method" ], "new_concepts": [], "current_concepts": [ "Factoring Trinomials", "Factoring by Grouping", "AC Method" ] } ## Identify the coefficients Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &2y^2 + 13y + 15\ &a = 2,\quad b = 13,\quad c = 15 \end{aligned} $$ ## Find two numbers that multiply to ac and add to b Using the *AC Method* knowledge point $$ \begin{aligned} &a \cdot c = 2 \cdot 15 = 30\ &p \cdot q = 30,\quad p + q = 13\ &p = 10,\quad q = 3 \end{aligned} $$ ## Rewrite the middle term and factor by grouping Using the *Factoring by Grouping* knowledge point $$ \begin{aligned} &2y^2 + 10y + 3y + 15\ &2y(y + 5) + 3(y + 5)\ &(2y + 3)(y + 5) \end{aligned} $$ Factor. $2y^2 + 13y + 15 =$ $(2y + 3)(y + 5)$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Trinomials" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the coefficients

Find two numbers that multiply to ac and add to b

Rewrite the middle term and factor by grouping

Answer: