9. A student practices calculating the remainder when a cubic polynomial $f ( x )$ is divided by a linear polynomial $g ( x )$. It is known that the coefficient of the cubic term of $f ( x )$ is 3, and the coefficient of the linear term is 2. Student A mistakenly read the coefficient of the cubic term of $f ( x )$ as 2 (other coefficients were read correctly), and Student B mistakenly read the coefficient of the linear term of $f ( x )$ as $- 2$ (other coefficients were read correctly). The remainders calculated by Student A and Student B happen to be the same. Which of the following linear expressions could $g ( x )$ equal?
(1) $x$
(2) $x - 1$
(3) $x - 2$
(4) $x + 1$
(5) $x + 2$

A person calculates the remainder when the polynomial $f(x) = x^{3} + ax^{2} + bx + c$ is divided by $g(x) = ax^{3} + bx^{2} + cx + d$, where $a, b, c, d$ are real numbers and $a \neq 0$. He mistakenly read it as $g(x)$ divided by $f(x)$, and after calculation obtained the remainder as $-3x - 17$. Assuming the correct remainder when $f(x)$ is divided by $g(x)$ equals $px^{2} + qx + r$, what is the value of $p$?
(1) $-3$ (2) $-1$ (3) $0$ (4) $2$ (5) $3$

Given that $t ^ { 3 } - 2 = 0$, which of the following is the equivalent of $\frac { 1 } { t ^ { 2 } + t + 1 }$ in terms of $t$?
A) $t + 1$
B) $\mathrm { t } - 2$
C) $t - 1$
D) $t ^ { 2 } + 1$
E) $t ^ { 2 } + 3$

Real coefficient polynomials $P ( x ) , Q ( x )$ and $R ( x )$ are given. For the polynomial $\mathrm { P } ( \mathrm { x } )$ whose constant term is nonzero,
$$P ( x ) = Q ( x ) \cdot R ( x + 1 )$$
the equality is satisfied. If the constant term of P is twice the constant term of Q, what is the sum of the coefficients of R?
A) $\frac { 2 } { 3 }$
B) $\frac { 1 } { 4 }$
C) $\frac { 3 } { 4 }$
D) 1
E) 2