Question

4
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?
-2m³ + m² - m +

Explanation:

Step1: Recall the Remainder Theorem

The Remainder Theorem states that if a polynomial \( f(m) \) is divided by \( (m - a) \), the remainder is \( f(a) \). Here, we are dividing by \( (m + 1) \), which can be written as \( (m - (-1)) \), so \( a=-1 \). Since the remainder is 0, \( f(-1)=0 \).

Step2: Define the polynomial

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

Step3: Substitute \( m = -1 \) into the polynomial

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

$$
LATEXBLOCK0
$$

Step4: Solve for \( c \)

Since \( f(-1) = 0 \) (because the remainder is 0), we set up the equation:

$$ 4 + c=0 $$

Subtract 4 from both sides:

$$ c=-4 $$

Answer:

\(-4\)