P(x)=2x^(4)-x^(3)+2x^(2)-6 What is the remainder when P(x) is divided by (x-2) ?

Problem Understanding: Understand the problem. We need to find the remainder when the polynomial P(x) = 2x^4 - x^3 + 2x^2 - 6 is divided by the binomial (x - 2).Remainder Theorem: Apply the Remainder Theorem. The Remainder Theorem states that if a polynomial P(x) is divided by (x - c), the remainder is P(c). Here, c = 2.Substituting x = 2: Substitute x = 2 into P(x). P(2) = 2(2)^4 - (2)^3 + 2(2)^2 - 6Calculating P(2): Calculate P(2). P(2) = 2(16) - 8 + 2(4) - 6 P(2) = 32 - 8 + 8 - 6 P(2) = 24 + 2 P(2) = 26

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P(x)=2x^(4)-x^(3)+2x^(2)-6
What is the remainder when
P(x) is divided by
(x-2) ?

$P(x)=2 x^{4}-x^{3}+2 x^{2}-6$ $\newline$ What is the remainder when $P(x)$ is divided by $(x-2)$ ?

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Math Problems

Algebra 2

Composition of linear and quadratic functions: find a value

Full solution

P(x)=2 x^{4}-x^{3}+2 x^{2}-6

\newline

What is the remainder when

P(x)

is divided by

(x-2)

Problem Understanding: Understand the problem. $\newline$ We need to find the remainder when the polynomial $P(x) = 2x^4 - x^3 + 2x^2 - 6$ is divided by the binomial $(x - 2)$ .
Remainder Theorem: Apply the Remainder Theorem. $\newline$ The Remainder Theorem states that if a polynomial $P(x)$ is divided by $(x - c)$ , the remainder is $P(c)$ . $\newline$ Here, $c = 2$ .
Substituting $x = 2$ : Substitute $x = 2$ into $P(x)$ . $P(2) = 2(2)^4 - (2)^3 + 2(2)^2 - 6$
Calculating $P(2)$ : Calculate $P(2)$ .
$P(2) = 2(16) - 8 + 2(4) - 6$
$P(2) = 32 - 8 + 8 - 6$
$P(2) = 26$