completely factor the given trinomial.

\8a^2b - 44ab + 20b\

Question

completely factor the given trinomial.

\8a^2b - 44ab + 20b\

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 Polynomials by GCF", "Factoring Trinomials" ], "new_concepts": [], "current_concepts": [ "Factoring Polynomials by GCF", "Factoring Trinomials" ] } ## Factor out the greatest common factor Using the *Factoring Polynomials by GCF* knowledge point $$ \begin{aligned} \text{GCF}(8a^2b, -44ab, 20b) &= 4b \ 8a^2b - 44ab + 20b &= 4b(2a^2 - 11a + 5) \end{aligned} $$ ## Factor the remaining quadratic trinomial Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} 2a^2 - 11a + 5 &= 2a^2 - 10a - a + 5 \ &= 2a(a - 5) - 1(a - 5) \ &= (2a - 1)(a - 5) \end{aligned} $$ ## Combine all factored parts Using the *Factoring Trinomials* and *Factoring Polynomials by GCF* knowledge points $$ 8a^2b - 44ab + 20b = 4b(2a - 1)(a - 5) $$ Completely factor the given trinomial. $4b(2a - 1)(a - 5)$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Polynomials" ] }

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QUESTION IMAGE

Question

Explanation:

Factor out the greatest common factor

Factor the remaining quadratic trinomial

Combine all factored parts

Answer: