completely factor the polynomial, if possible.

\4xy^2 + 28xy + 49x\

Question

completely factor the polynomial, if possible.

\4xy^2 + 28xy + 49x\

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", "Square of a Binomial Sum" ], "new_concepts": [], "current_concepts": [ "Factoring Polynomials by GCF", "Square of a Binomial Sum", "Factoring Trinomials" ] } ## Identify the greatest common factor Using the *Factoring Polynomials by GCF* knowledge point $$ \begin{aligned} &\text{Polynomial: } 4xy^2 + 28xy + 49x\ &\text{GCF of terms: } \text{gcd}(4xy^2, 28xy, 49x) = x\ &4xy^2 + 28xy + 49x = x(4y^2 + 28y + 49) \end{aligned} $$ ## Factor the remaining trinomial Using the *Square of a Binomial Sum* knowledge point $$ \begin{aligned} &4y^2 + 28y + 49 = (2y)^2 + 2(2y)(7) + 7^2\ &4y^2 + 28y + 49 = (2y + 7)^2 \end{aligned} $$ ## Write the completely factored form Using the *Square of a Binomial Sum* and *Factoring Polynomials by GCF* knowledge points $$ 4xy^2 + 28xy + 49x = x(2y + 7)^2 $$ $x(2y + 7)^2$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Polynomials by GCF" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the greatest common factor

Factor the remaining trinomial

Write the completely factored form

Answer: