if $f(x) = x^4 - x^3 + x^2$ and $g(x) = -x^2$, where $x \
eq 0$, what is $(f/g)(x)$?

$x^2 - x + 1$
$x^2 + x + 1$
$-x^2 + x - 1$
$-x^2 - x - 1$

Question

if $f(x) = x^4 - x^3 + x^2$ and $g(x) = -x^2$, where $x \
eq 0$, what is $(f/g)(x)$?

$x^2 - x + 1$
$x^2 + x + 1$
$-x^2 + x - 1$
$-x^2 - x - 1$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Function Division", "Polynomial Division" ], "current_concepts": [ "Function Division", "Polynomial Division" ] } ## Define the function division $$ (f/g)(x) = \frac{f(x)}{g(x)} $$ ## Substitute the given functions $$ (f/g)(x) = \frac{x^4 - x^3 + x^2}{-x^2},\quad x eq 0 $$ ## Simplify the expression $$ (f/g)(x) = \frac{x^4}{-x^2} - \frac{x^3}{-x^2} + \frac{x^2}{-x^2} = -x^2 + x - 1 $$

(A) $x^2 - x + 1$

(B) $x^2 + x + 1$

(C) $-x^2 + x - 1$

(D) $-x^2 - x - 1$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Function Division" ] }

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QUESTION IMAGE

Question

Explanation:

Define the function division

Substitute the given functions

Simplify the expression

Answer: