question 1
find the greatest common factor: $50x^3y^6, 4x^5y^7, 10x^4y^7$
- $2xy^6$
- $5x^4y^6$
- $10x^3y^7$
- $2x^3y^6$

question 2
factor completely: $4q^2rt - 2q^3r^2v + 8qr^2s$
- $2r(2q^2t - q^3rv + 4qrs)$
- $2(4q^2rt - q^3r^2v + 4qr^2s)$
- $-2qr(2qt + q^2rv - 4rs)$
- $2qr(2qt - q^2rv + 4rs)$

question 3
factor the following polynomial expression completely: $x(x + 3) + 6(x + 3)$
- $(x - 6)(x - 3)$
- $(x - 6)(x + 3)$
- $(x + 6)(x + 3)$
- $(x + 6)(x + 3)^2$

question 4
factor the following expression completely by grouping: $x^2 + 3x + 6x + 18$
- $(6x + 3)(x + 6)$
- $(x - 6)(x + 3)$
- $(x + 6)(x + 3)$
- $(x + 6)(x + 3)^2$

Question

question 1
find the greatest common factor: $50x^3y^6, 4x^5y^7, 10x^4y^7$
- $2xy^6$
- $5x^4y^6$
- $10x^3y^7$
- $2x^3y^6$

question 2
factor completely: $4q^2rt - 2q^3r^2v + 8qr^2s$
- $2r(2q^2t - q^3rv + 4qrs)$
- $2(4q^2rt - q^3r^2v + 4qr^2s)$
- $-2qr(2qt + q^2rv - 4rs)$
- $2qr(2qt - q^2rv + 4rs)$

question 3
factor the following polynomial expression completely: $x(x + 3) + 6(x + 3)$
- $(x - 6)(x - 3)$
- $(x - 6)(x + 3)$
- $(x + 6)(x + 3)$
- $(x + 6)(x + 3)^2$

question 4
factor the following expression completely by grouping: $x^2 + 3x + 6x + 18$
- $(6x + 3)(x + 6)$
- $(x - 6)(x + 3)$
- $(x + 6)(x + 3)$
- $(x + 6)(x + 3)^2$

Accepted Answer

{ "quality": "clear", "question_count": 4, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Greatest Common Factor", "Factoring by Grouping" ], "new_concepts": [], "current_concepts": [ "Greatest Common Factor", "Factoring by Grouping", "Factoring Polynomials" ] } ## Find the greatest common factor of the terms in Question 1 $$ \begin{aligned} &\text{Terms: } 50x^3y^6, \quad 4x^4y^7, \quad 10x^3y^7 \ &\text{GCF of coefficients } (50, 4, 10) = 2 \ &\text{GCF of } x \text{ terms } (x^3, x^4, x^3) = x^3 \ &\text{GCF of } y \text{ terms } (y^6, y^7, y^7) = y^6 \ &\text{GCF} = 2x^3y^6 \end{aligned} $$ ## Factor the expression in Question 2 completely $$ \begin{aligned} &\text{Expression: } 4q^2rt - 2q^3r^2v + 8qr^2s \ &\text{GCF of terms: } 2qr \ &\text{Factored form: } 2qr(2qt - q^2rv + 4rs) \end{aligned} $$ ## Factor the polynomial in Question 3 completely $$ \begin{aligned} &\text{Expression: } x(x + 3) + 6(x + 3) \ &\text{Common binomial factor: } (x + 3) \ &\text{Factored form: } (x + 6)(x + 3) \end{aligned} $$ ## Factor the expression in Question 4 by grouping $$ \begin{aligned} &\text{Expression: } x^2 + 3x + 6x + 18 \ &\text{Group terms: } (x^2 + 3x) + (6x + 18) \ &\text{Factor each group: } x(x + 3) + 6(x + 3) \ &\text{Factored form: } (x + 6)(x + 3) \end{aligned} $$ ## Question 1 (A) $2x^3y^6$

(B) $5x^4y^6$

(C) $10x^3y^7$

(D) $2x^3y^7$ ## Question 2 (A) $2r(2q^2t - q^3rv + 4qrs)$

(B) $2(4q^2rt - q^3r^2v + 4qr^2s)$

(C) $-2qr(2qt + q^2rv - 4rs)$

(D) $2qr(2qt - q^2rv + 4rs)$ ## Question 3 (A) $(x - 6)(x - 3)$

(B) $(x - 6)(x + 3)$

(C) $(x + 6)(x + 3)$

(D) $(x + 6)(x + 3)^2$ ## Question 4 (A) $(6x + 3)(x + 6)$

(B) $(x - 6)(z + 3)$

(C) $(x + 6)(x + 3)$

(D) $(x + 6)(x + 3)^2$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Polynomials" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Find the greatest common factor of the terms in Question 1

Factor the expression in Question 2 completely

Factor the polynomial in Question 3 completely

Factor the expression in Question 4 by grouping

Answer:

Question 1

Question 2

Question 3

Question 4