completely factor the given trinomial.

\6a^2b - 21ab + 9b\

Question

completely factor the given trinomial.

\6a^2b - 21ab + 9b\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Factoring Polynomials by GCF", "Factoring Trinomials" ], "new_concepts": [], "current_concepts": [ "Factoring Polynomials by GCF", "Factoring Trinomials" ] } ## Find the greatest common factor Using the *Factoring Polynomials by GCF* knowledge point $$ \begin{aligned} &\text{Terms: } 6a^2b,\; -21ab,\; 9b\ &\text{GCF of coefficients (6, -21, 9): } 3\ &\text{GCF of variable parts: } b\ &\text{Overall GCF: } 3b\ &6a^2b - 21ab + 9b = 3b(2a^2 - 7a + 3) \end{aligned} $$ ## Factor the remaining quadratic trinomial Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &\text{Trinomial: } 2a^2 - 7a + 3\ &\text{Find factors of } 2 \times 3 = 6 \text{ that sum to } -7: -6 \text{ and } -1\ &2a^2 - 6a - a + 3 = 2a(a - 3) - 1(a - 3)\ &(2a - 1)(a - 3) \end{aligned} $$ ## Combine all factors Using the *Factoring Polynomials by GCF* and *Factoring Trinomials* knowledge points $$ 3b(2a - 1)(a - 3) $$ $3b(2a - 1)(a - 3)$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Polynomials by GCF" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Find the greatest common factor

Factor the remaining quadratic trinomial

Combine all factors

Answer: