P(x)=2x^(4)-x^(3)+2x^(2)-k where k is an unknown integer. P(x) divided by (x+1) has a remainder of 2 . What is the value of k ? k=

Apply Remainder Theorem: To find the value of k, we will use the Remainder Theorem, which states that if a polynomial P(x) is divided by (x - c), the remainder is P(c). Since we are dividing by (x + 1), we will find P(-1).Substitute x = -1: Substitute x = -1 into the polynomial P(x) = 2x^4 - x^3 + 2x^2 - k. P(-1) = 2(-1)^4 - (-1)^3 + 2(-1)^2 - k P(-1) = 2(1) - (-1) + 2(1) - k P(-1) = 2 + 1 + 2 - k P(-1) = 5 - kSet P(-1) equal to 2: According to the problem, the remainder when P(x) is divided by (x + 1) is 2. Therefore, we set P(-1) equal to 2. 5 - k = 2Solve for k: Solve for k. 5 - k = 2 k = 5 - 2 k = 3

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P(x)=2x^(4)-x^(3)+2x^(2)-k
where
k is an unknown integer.

P(x) divided by
(x+1) has a remainder of 2 .
What is the value of
k ?

k=

$P(x)=2 x^{4}-x^{3}+2 x^{2}-k$ $\newline$ where $k$ is an unknown integer. $\newline$ $P(x)$ divided by $(x+1)$ has a remainder of $2$ . $\newline$ What is the value of $k$ ? $\newline$ $k=$

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Algebra 2

Evaluate recursive formulas for sequences

Full solution

P(x)=2 x^{4}-x^{3}+2 x^{2}-k

\newline

where

k

is an unknown integer.

\newline

P(x)

divided by

(x+1)

has a remainder of

2

\newline

What is the value of

k

\newline

k=

Apply Remainder Theorem: To find the value of $k$ , we will use the Remainder Theorem, which states that if a polynomial $P(x)$ is divided by $(x - c)$ , the remainder is $P(c)$ . Since we are dividing by $(x + 1)$ , we will find $P(-1)$ .
Substitute $x = -1$ : Substitute $x = -1$ into the polynomial $P(x) = 2x^4 - x^3 + 2x^2 - k$ . $\newline$ $P(-1) = 2(-1)^4 - (-1)^3 + 2(-1)^2 - k$ $\newline$ $P(-1) = 2(1) - (-1) + 2(1) - k$ $\newline$ $P(-1) = 2 + 1 + 2 - k$ $\newline$ $P(-1) = 5 - k$
Set $P(-1)$ equal to $2$ : According to the problem, the remainder when $P(x)$ is divided by $(x + 1)$ is $2$ . Therefore, we set $P(-1)$ equal to $2$ . $\newline$ $5 - k = 2$
Solve for k: Solve for k. $\newline$ $5 - k = 2$ $\newline$ $k = 5 - 2$ $\newline$ $k = 3$