select the correct answer from the drop-down menu.

when this polynomial is divided by $(m + 1)$, the remainder is 0. what is the value of the polynomials constant term?

$-2m^3 + m^2 - m + \text{choose an answer}$

Question

select the correct answer from the drop-down menu.

when this polynomial is divided by $(m + 1)$, the remainder is 0. what is the value of the polynomials constant term?

$-2m^3 + m^2 - m + \text{choose an answer}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Remainder Theorem", "Polynomial Term Identification" ], "new_concepts": [], "current_concepts": [ "Remainder Theorem", "Polynomial Term Identification", "Solving Linear Equations" ] } ## Define the polynomial and divisor $$ \begin{aligned} &P(m) = -2m^3 + m^2 - m + c\ &\text{Divisor: } m + 1 \implies m = -1 \end{aligned} $$ ## Apply the Remainder Theorem $$ \begin{aligned} &P(-1) = 0\ &-2(-1)^3 + (-1)^2 - (-1) + c = 0\ &-2(-1) + 1 + 1 + c = 0\ &2 + 1 + 1 + c = 0 \end{aligned} $$ ## Solve for the constant term $$ \begin{aligned} &4 + c = 0\ &c = -4 \end{aligned} $$ When this polynomial is divided by $(m + 1)$, the remainder is 0. What is the value of the polynomial's constant term? $-2m^3 + m^2 - m + $ -4 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Remainder Theorem" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Define the polynomial and divisor

Apply the Remainder Theorem

Solve for the constant term

Answer: