10 4-factoring trinomials with a nontrivi
(1 point)

factor the given polynomial.

(5r^2 + 8rx - 21x^2 =)

if the expression cannot be factored then answer with prime.

Question

10 4-factoring trinomials with a nontrivi
(1 point)

factor the given polynomial.

(5r^2 + 8rx - 21x^2 =)

if the expression cannot be factored then answer with prime.

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": [ "Polynomial Factoring", "Factoring Trinomials" ], "new_concepts": [ "Factoring Trinomials with Two Variables" ], "current_concepts": [ "Polynomial Factoring", "Factoring Trinomials", "Factoring Trinomials with Two Variables" ] } ## Identify coefficients and product-sum targets Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &5r^2 + 8rx - 21x^2\ &a = 5,\quad b = 8,\quad c = -21\ &\text{Product } ac = 5 \times (-21) = -105\ &\text{Sum } b = 8 \end{aligned} $$ ## Find factors of the product that sum to the target Using the *Polynomial Factoring* knowledge point $$ \begin{aligned} &-105 = 15 \times (-7)\ &15 + (-7) = 8 \end{aligned} $$ ## Rewrite the middle term and factor by grouping Using the *Polynomial Factoring* knowledge point $$ \begin{aligned} &5r^2 + 15rx - 7rx - 21x^2\ &= 5r(r + 3x) - 7x(r + 3x)\ &= (5r - 7x)(r + 3x) \end{aligned} $$ Factor the given polynomial. $5r^2 + 8rx - 21x^2 =$ $(5r - 7x)(r + 3x)$ If the expression cannot be factored then answer with prime. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Factoring" ] }

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QUESTION IMAGE

Question

Explanation:

Identify coefficients and product-sum targets

Find factors of the product that sum to the target

Rewrite the middle term and factor by grouping

Answer: