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