The polynomial function f is defined as f(m)=(m^(3)-m^(2)-17 m-15)(m+1). When f(m) is divided by (m+1), what is the remainder?

Apply Remainder Theorem: To find the remainder when f(m) is divided by (m+1), we can use the Remainder Theorem which states that the remainder of the division of a polynomial f(x) by (x - c) is f(c).Substitute m with -1: In this case, we need to find f(-1) because we are dividing by (m+1), which is the same as (m - (-1)).Simplify the expression: Now, let's substitute m with -1 in the polynomial f(m) = (m^3 - m^2 - 17m - 15)(m + 1).f(-1) = ((-1)^3 - (-1)^2 - 17(-1) - 15)(-1 + 1).Simplify the expression: f(-1) = ((-1) - (1) + 17 - 15)(0).f(-1) = (0)(0) = 0.

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The polynomial function
f is defined as
f(m)=(m^(3)-m^(2)-17 m-15)(m+1). When
f(m) is divided by
(m+1), what is the remainder?

The polynomial function $f$ is defined as $f(m)=\left(m^{3}-m^{2}-17 m-15\right)(m+1)$ . When $f(m)$ is divided by $(m+1)$ , what is the remainder?

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Q. The polynomial function

f

is defined as

f(m)=\left(m^{3}-m^{2}-17 m-15\right)(m+1)

. When

f(m)

is divided by

(m+1)

, what is the remainder?

Apply Remainder Theorem: To find the remainder when $f(m)$ is divided by $(m+1)$ , we can use the Remainder Theorem which states that the remainder of the division of a polynomial $f(x)$ by $(x - c)$ is $f(c)$ .
Substitute $m$ with $-1$ : In this case, we need to find $f(-1)$ because we are dividing by $(m+1)$ , which is the same as $(m - (-1))$ .
Simplify the expression: Now, let's substitute $m$ with $-1$ in the polynomial $f(m) = (m^3 - m^2 - 17m - 15)(m + 1)$ .
Simplify the expression: Now, let's substitute $m$ with $-1$ in the polynomial $f(m) = (m^3 - m^2 - 17m - 15)(m + 1)$ . $f(-1) = ((-1)^3 - (-1)^2 - 17(-1) - 15)(-1 + 1)$ .
Simplify the expression: Now, let's substitute $m$ with $-1$ in the polynomial $f(m) = (m^3 - m^2 - 17m - 15)(m + 1)$ . $f(-1) = ((-1)^3 - (-1)^2 - 17(-1) - 15)(-1 + 1)$ .Simplify the expression: $f(-1) = ((-1) - (1) + 17 - 15)(0)$ .
Simplify the expression: Now, let's substitute $m$ with $-1$ in the polynomial $f(m) = (m^3 - m^2 - 17m - 15)(m + 1)$ . $f(-1) = ((-1)^3 - (-1)^2 - 17(-1) - 15)(-1 + 1)$ .Simplify the expression: $f(-1) = ((-1) - (1) + 17 - 15)(0)$ . $f(-1) = (0)(0) = 0$ .