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x-2Question 8 of 15Use the remainder theorem to find P (2) for P (x)=xª − 3x³ +x−9.-(2,01 mismoSpecifically, give the quotient and the remainder for the associated division and the value of P (2)_Quotient =RemainderP (2)=

x2Question 8 of 15Use the remainder theorem to find P 2 for P xxª 3x x9201 mismoSpecifically give the quotient and the remainder for the associated division and class=

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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]

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