8)
The remainder theorem states that when a polynomial P(x) is divided by a linear polynomial x-b, the remainder is given by r=P(b).
Thus, in our case,
[tex]P(2)=2^4-3(2)^3+2-9=16-24+2-9=-15[/tex]
Then, the Remainder theorem states that if we divide P(x) by x-2, the remainder will be -15.
Calculating the quotient of P(x)/(x-2),
Hence, the answers are
[tex]\begin{gathered} Q(x)=x^3-x^2-2x-3 \\ Remainder=-15 \\ P(2)=-15 \end{gathered}[/tex]
