For the given polynomial P(x) and the given c, use the remainder theorem to find P(c).
-$P ( x ) = - 2 x ^ { 2 } - 7 x - 9 ; \frac { 1 } { 3 }$
A) $- \frac { 104 } { 9 }$
B) 2
C) $\frac { 104 } { 9 }$
D) $- 2$

Question

Quizplus · Accepted Answer

The remainder theorem states that if a polynomial $P(x)$ is divided by $x - c$, the remainder is $P(c)$. Substituting $c = \frac{1}{3}$ into $P(x) = -2x^2 - 7x - 9$, we get $P\left(\frac{1}{3}\right) = -2\left(\frac{1}{3}\right)^2 - 7\left(\frac{1}{3}\right) - 9 = -2\left(\frac{1}{9}\right) - \frac{7}{3} - 9 = -\frac{2}{9} - \frac{7}{3} - 9 = -\frac{2}{9} - \frac{21}{9} - \frac{81}{9} = -\frac{104}{9}$.

For the Given Polynomial P(x) and the Given C, Use P(x)=−2x2−7x−9;13P ( x ) = - 2 x ^ { 2 } - 7 x - 9 ; \frac { 1 } { 3 }P(x)=−2x2−7x−9;31​

For the Given Polynomial P(x) and the Given C, Use $P ( x ) = - 2 x ^ { 2 } - 7 x - 9 ; \frac { 1 } { 3 }$