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

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 - a), the remainder is P(a). Here, we need to find the remainder when P(x) is divided by (x - 3), so we will calculate P(3).Substituting x = 3: Substitute x = 3 into the polynomial P(x). P(x) = x^4 - 2x^3 - 3x^2 + 4 P(3) = (3)^4 - 2(3)^3 - 3(3)^2 + 4Calculating P(3): Calculate the value of P(3). P(3) = (3)^4 - 2(3)^3 - 3(3)^2 + 4 P(3) = 81 - 2(27) - 3(9) + 4 P(3) = 81 - 54 - 27 + 4Finding the Remainder: Finish the calculation to find the remainder. P(3) = 81 - 54 - 27 + 4 P(3) = 27 - 27 + 4 P(3) = 0 + 4 P(3) = 4

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

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

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Math Problems

Algebra 2

Composition of linear and quadratic functions: find a value

Full solution

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

\newline

What is the remainder when

P(x)

is divided by

(x-3)

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 $(x - a)$ , the remainder is $P(a)$ . $\newline$ Here, we need to find the remainder when $P(x)$ is divided by $(x - 3)$ , so we will calculate $P(3)$ .
Substituting $x = 3$ : Substitute $x = 3$ into the polynomial $P(x)$ .
$P(x) = x^4 - 2x^3 - 3x^2 + 4$
$P(3) = (3)^4 - 2(3)^3 - 3(3)^2 + 4$
Calculating P( $3$ ): Calculate the value of P( $3$ ). $\newline$ P( $3$ ) = $(3)^4 - 2(3)^3 - 3(3)^2 + 4$ $\newline$ P( $3$ ) = $81 - 2(27) - 3(9) + 4$ $\newline$ P( $3$ ) = $81 - 54 - 27 + 4$
Finding the Remainder: Finish the calculation to find the remainder. $\newline$ $P(3) = 81 - 54 - 27 + 4$ $\newline$ $P(3) = 27 - 27 + 4$ $\newline$ $P(3) = 0 + 4$ $\newline$ $P(3) = 4$