let (f(x) = x^3 - 27) use the factor theorem to help answer the following questions.

a) is (x - 27) a factor of (f(x))?
- yes
- no

b) is (x - 3) a factor of (f(x))?
- yes
- no

c) is (x + 3) a factor of (f(x))?
- yes
- no

Question

let (f(x) = x^3 - 27) use the factor theorem to help answer the following questions.

a) is (x - 27) a factor of (f(x))?
- yes
- no

b) is (x - 3) a factor of (f(x))?
- yes
- no

c) is (x + 3) a factor of (f(x))?
- yes
- no

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Factor Theorem", "Polynomial Factors" ], "current_concepts": [ "Factor Theorem", "Polynomial Factors" ] } ## Evaluate $f(27)$ to test the factor $x - 27$ $$ \begin{aligned} f(x) &= x^3 - 27 \ f(27) &= 27^3 - 27 = 19683 - 27 = 19656 eq 0 \end{aligned} $$ ## Evaluate $f(3)$ to test the factor $x - 3$ $$ \begin{aligned} f(3) &= 3^3 - 27 = 27 - 27 = 0 \end{aligned} $$ ## Evaluate $f(-3)$ to test the factor $x + 3$ $$ \begin{aligned} f(-3) &= (-3)^3 - 27 = -27 - 27 = -54 eq 0 \end{aligned} $$ ## Question 1 Yes No ## Question 2 Yes No ## Question 3 Yes

No

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Factor Theorem" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Evaluate \(f(27)\) to test the factor \(x - 27\)

Evaluate \(f(3)\) to test the factor \(x - 3\)

Evaluate \(f(-3)\) to test the factor \(x + 3\)

Answer:

Question 1

Question 2

Question 3