select all the correct answers.

\
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-5 & 0 \\
-4 & 240 \\
-3 & 0 \\
-1 & -240 \\
4 & 0 \\
5 & 960 \\
\hline
\end{array}
\

- $x + 5$
- $x - 5$
- $x + 3$
- $x - 3$
- $x + 4$
- $x - 4$

Question

select all the correct answers.

\
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-5 & 0 \\
-4 & 240 \\
-3 & 0 \\
-1 & -240 \\
4 & 0 \\
5 & 960 \\
\hline
\end{array}
\

- $x + 5$
- $x - 5$
- $x + 3$
- $x - 3$
- $x + 4$
- $x - 4$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Remainder Theorem" ], "new_concepts": [ "Factor Theorem" ], "current_concepts": [ "Remainder Theorem", "Factor Theorem" ] } ## Identify the zeros of the polynomial function $$ \begin{aligned} &f(-5) = 0 \ &f(-3) = 0 \ &f(4) = 0 \end{aligned} $$ ## Apply the Factor Theorem $$ \begin{aligned} &f(c) = 0 \iff (x - c) \text{ is a factor of } f(x) \ &f(-5) = 0 \implies (x - (-5)) = x + 5 \text{ is a factor} \ &f(-3) = 0 \implies (x - (-3)) = x + 3 \text{ is a factor} \ &f(4) = 0 \implies (x - 4) \text{ is a factor} \end{aligned} $$ ## Match with the given options $$ \begin{aligned} &\text{Correct factors: } x + 5,\ x + 3,\ x - 4 \end{aligned} $$

$x + 5$

$x - 5$

$x + 3$

$x - 3$

$x + 4$

$x - 4$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the zeros of the polynomial function

Apply the Factor Theorem

Match with the given options

Answer: