P(x)=3x^(4)-2x^(3)+2x^(2)-1 What is the remainder when P(x) is divided by (x+1) ?

Problem and Remainder Theorem: Understand the problem and the remainder theorem. The remainder theorem 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 can use the remainder theorem by finding P(-1).Substituting x = -1: Substitute x = -1 into the polynomial P(x). P(x) = 3x^4 - 2x^3 + 2x^2 - 1 P(-1) = 3(-1)^4 - 2(-1)^3 + 2(-1)^2 - 1Calculating P(-1): Calculate the value of P(-1). P(-1) = 3(1) - 2(-1) + 2(1) - 1 P(-1) = 3 + 2 + 2 - 1Simplifying the Expression: Simplify the expression to find the remainder. P(-1) = 3 + 2 + 2 - 1 P(-1) = 7 - 1 P(-1) = 6

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P(x)=3x^(4)-2x^(3)+2x^(2)-1
What is the remainder when
P(x) is divided by
(x+1) ?

$P(x)=3 x^{4}-2 x^{3}+2 x^{2}-1$ $\newline$ What is the remainder when $P(x)$ is divided by $(x+1)$ ?

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Math Problems

Algebra 2

Composition of linear and quadratic functions: find a value

Full solution

P(x)=3 x^{4}-2 x^{3}+2 x^{2}-1

\newline

What is the remainder when

P(x)

is divided by

(x+1)

Problem and Remainder Theorem: Understand the problem and the remainder theorem. $\newline$ The remainder theorem 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 can use the remainder theorem by finding $P(-1)$ .
Substituting $x = -1$ : Substitute $x = -1$ into the polynomial $P(x)$ .
$P(x) = 3x^4 - 2x^3 + 2x^2 - 1$
$P(-1) = 3(-1)^4 - 2(-1)^3 + 2(-1)^2 - 1$
Calculating $P(-1)$ : Calculate the value of $P(-1)$ .
$P(-1) = 3(1) - 2(-1) + 2(1) - 1$
$P(-1) = 3 + 2 + 2 - 1$
Simplifying the Expression: Simplify the expression to find the remainder. $\newline$ $P(-1) = 3 + 2 + 2 - 1$ $\newline$ $P(-1) = 7 - 1$ $\newline$ $P(-1) = 6$