Question

Use the remainder theorem to find P (3) for P(x) = -2x³ + 6x² — 4x -4. Specifically, give the quotient and the remainder for the associated division and the value of P (3) Quotient = Remainder =p(3) =

Answer 1

The polynomial P is given by:

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

Using the remainder theorem, the value of P(3) is given by:

$\begin{gathered} P(3)=-2\cdot\:3^3+6\cdot\:3^2-4\cdot\:3-4 \\ =-16 \end{gathered}$

The divisor is given by:

$x-3$

Since

$-2x^3+6x^2-4x-4=(x-3)(-2x^2-4)-16$

Therefore, the Quotient is:

$\begin{equation*} -2x^2-4 \end{equation*}$

And the remainder is:

$-16$

Quotient = -2x² - 4

Remainder = -16

P(3) = -16