consider the trinomial $9x^2 + 21x + 10$.

what value is placed on top of the x?
what value is placed on the bottom of the x?
what is the factored form of $9x^2 + 21x + 10$?

Question

consider the trinomial $9x^2 + 21x + 10$.

what value is placed on top of the x?
what value is placed on the bottom of the x?
what is the factored form of $9x^2 + 21x + 10$?

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [], "current_concepts": [ "X Method Factoring", "Factoring Trinomials" ] } ## Identify coefficients of the trinomial $$ \begin{aligned} &9x^2 + 21x + 10 \implies a = 9,\ b = 21,\ c = 10 \end{aligned} $$ ## Calculate values for the X method diagram $$ \begin{aligned} &\text{Top value: } ac = 9 \times 10 = 90\ &\text{Bottom value: } b = 21 \end{aligned} $$ ## Find factors and write the factored form $$ \begin{aligned} &\text{Find two numbers that multiply to } 90 \text{ and add to } 21: 15 \text{ and } 6\ &9x^2 + 21x + 10 = 9x^2 + 15x + 6x + 10 = 3x(3x + 5) + 2(3x + 5) = (3x + 5)(3x + 2) \end{aligned} $$ ## Question 1 What value is placed on top of the X? 90 ## Question 2 What value is placed on the bottom of the X? 21 ## Question 3 What is the factored form of $ 9x^2 + 21x + 10 $? $(3x + 5)(3x + 2)$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Polynomials" ] }

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QUESTION IMAGE

Question

Explanation:

Identify coefficients of the trinomial

Calculate values for the X method diagram

Find factors and write the factored form

Answer:

Question 1

Question 2

Question 3