Question

2
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 polynomial’s constant term?
-2m³ + m² - m +

Explanation:

Step1: Apply Remainder Theorem

The Remainder Theorem states that if a polynomial \( f(m) \) is divided by \( (m - a) \), the remainder is \( f(a) \). Here, we divide by \( (m + 1)=(m - (-1)) \), so \( a=-1 \). Since the remainder is 0, \( f(-1) = 0 \).

Let the polynomial be \( f(m)=-2m^{3}+m^{2}-m + c \) (where \( c \) is the constant term we need to find).

Step2: Substitute \( m = -1 \) into \( f(m) \)

Substitute \( m=-1 \) into \( f(m) \):

$$
LATEXBLOCK0
$$

Step3: Solve for \( c \)

Since \( f(-1) = 0 \) (remainder is 0), we set \( 4 + c = 0 \). Solving for \( c \), we get \( c=-4 \).

Answer:

-4